Ian McGeechan's men arrived at Coca Cola Park knowing a series victory was beyond them following heartbreaking defeats in Durban and Pretoria but they responded in the perfect manner as they produced a performance worthy of the famous red shirt.
The tourists were dominant throughout the entire 80 minutes as they seemed undaunted by the pressure of attempting to avoid becoming the first Lions side to be whitewashed on South Africa soil.
Williams struck twice in eight first-half minutes before Monye's interception try moved the Lions to within touching distance of a well-deserved victory following their last-minute reverse in Pretoria eight days earlier.
Two late penalties from Stephen Jones then put the game beyond the Boks in the final 10 minutes and allowed the thousands of travelling Lions supporters to celebrate a wonderful win on what most observers would agree has been a truly memorable tour.
Having missed his opening shot at goal from 45 metres out after just three minutes, Jones put the first points on the board five minutes later through a far easier attempt after the Lions had come out on top in the first scrummaging battle of the afternoon.
Much had been made of the reintroduction of Phil Vickery to face his first Test nemesis Tendai Mtawarira. The former England captain endured a torrid time at the hands of 'The Beast' during the first half of the opening international in Durban and was duly omitted from the crucial second encounter in Pretoria. Injury to Adam Jones led to a recall for this final rubber and Vickery started superbly, getting the better of his opposite man at the opening scrum. The immediate result was a penalty to the Lions 30 metres out and a 3-0 lead; the long-term impact was arguably even more important as Vickery sent out an immediate warning that he would not be bullied in the set piece.
Morne Steyn, South Africa's hero from last weekend's nail-biting affair (and quite possibly for the next 12 years), brought the hosts back on terms two minutes later, however, as the Bulls fly-half built on his 100-per-cent record with the boot in his two international starts to date.
The scores remained level until the first try of the match arrived a quarter of an hour later, but when that score did arrive the Lions support would have felt it was more than worth the wait.
Just as they had done in the second Test, it was the Lions who struck first. Ireland No8 Jamie Heaslip took possession on the Springbok 10-metre line and appeared to have been brought down before being able to get into his stride. But the Boks failed to hold on to their man and Heaslip regathered his footing and strode forward into the opposition 22. Just as a good winger should be, Shane Williams was then on hand to make the most of the gap opened up by the Heineken Cup winner as the Lions moved 8-3 in front with 25 minutes on the clock.
Williams touched down underneath the posts but Jones was unable to add the extras as the ball fell off the kicking tee after the Scarlets outside-half had begun his run up.
Having featured in nine of the 10 matchday squads without registering a single try on the current tour, Williams suddenly found himself with two to his name 15 minutes before half-time at the old Ellis Park..
The 2008 IRB World Player of the Year could not have been faulted for his effort on tour yet luck had not been on the 32-year-old's side prior to what could prove to his final outing in Lions colours. That all changed midway through the first half in South Africa's largest city as he followed up his first well-taken score with another poacher's effort to send the Lions into dreamland.
Veteran second row Simon Shaw continued with the same enthusiasm that had seen him claim the man-of-the-match award at Loftus Versfeld, winning turn over ball to set the platform for the Lions' and Williams' second score.
Shaw used his 12-and-a-half years' experience of international rugby to nick possession and the backline did the rest in impressive style. Halfbacks Mike Phillips and Jones moved the ball wide to Riki Flutey who planted the ball on his left foot on halfway and then into space behind the Boks' front line defence. The New Zealand born centre won the race to the bouncing ball before flicking it into the arms of Williams in one fluid motion.
The Welshman raced home unopposed from 25 metres out to reward the Lions for keeping the ball alive with yet another fine piece of enterprise.
Williams did well to hang on to Flutey's sublime pass as he reached behind him to ensure the Lions learned from their mistakes in the opening rubber when they created plenty of opportunities but failed to turn pressure into points.
With the Lions now two scores to the good, Jones made no mistake with the conversion as the ball remained on the tee until after he had made contact to stretch the lead to a comfortable 12 points at 15-3.
If the Lions had once again put themselves in the driving seat, they were given a timely reminder that the task at hand was far from finished on the stroke of half-time. Just as they had done a week earlier, the Boks had the final say of the first 40 minutes as they doubled their first-half tally with a late penalty. Last Saturday it was Frans Steyn who brought his country back to 16-8 with the final play off the half and this time it was his namesake Morne who did exactly the same to cut the Lions' first period lead to 15-6.
The end-to-end nature of the opening 40 minutes continued after the break, with the impressive Rob Kearney and Springbok replacement Frans Steyn missing a long-range penalty and an even longer-range drop goal earlier in the second half with both sides knowing the first score of the second period could prove crucial.
Fortunately for the Lions, that vital next score went their way when it could so easily have been the Springboks celebrating.
With Peter de Villiers' side in possession deep in Lions territory, inside centre Wynard Olivier threw a lengthy pass as the Boks looked to exploit space out wide. Monye read the Bulls star's intentions perfectly, extending an arm and preventing South Africa from putting the Lions under considerable pressure on the edge of their own 22.
The Harlequins wing had been heavily criticised for his failure to take two try-scoring chances at the ABSA Stadium a fortnight ago but this time he created something out of nothing and supplied an accomplished finish from fully 80 metres out.
Only opposite number Jongi Nokwe gave chase but even the fastest man on the field couldn't catch Monye, who raised his arms to salute the Lions' Red Army before diving over the line directly underneath the uprights.
A second conversion from Jones moved the Lions three scores clear at 22-6 with 26 minutes remaining as the Lions continued to grow in confidence.
It was a similar lead to that enjoyed by the Springboks with the same amount of time left in the first Test but, unlike their opponents, the Lions never looked like letting the advantage slip.
Morne Steyn did reduce the gap to 15 points with his third successful penalty and Odwa Ndungane had a try ruled out by the television match official for a foot in touch, but the Lions always appeared to be in control even as the effects of altitude should have been setting in during the closing stages.
Penalties in the 70th and 72nd minutes from Jones put the result beyond doubt and the Lions could finally smile the kind of smiles that had so far eluded them in the three-match series.
Twice they had come so close to a Test victory in their two previous attempts yet twice they had fallen short. Twice victory looked as though it might be on the cards only for defeat to rear its ugly head. Today's performance was just as impressive as the closing stages in Durban and the opening half in Pretoria but the difference was that the Lions maintained their composure and exerted their dominance for the full 80 minutes. The Boks weren't allowed to build their decisive first Test lead nor were they were given the opportunity to complete their stunning second Test comeback. Today was simply all about the Lions.
Now the huge disappointments of the first two Tests can finally be put behind Britain and Ireland's elite as the Lions build for Australia in 2013. The latest Lions series may once again have gone the way the way of the southern hemisphere giants but while the Boks ultimately won the war, there can be no doubting the victors in today's mammoth battle.