Ian McGeechan's men outscored their hosts by three tries to one but were left to rely on a 77th-minute penalty from replacement full back James Hook on a wet and windy afternoon at Newlands.
First-half scores from Tommy Bowe and Ugo Monye, together with a 55th-minute effort from Martyn Williams and eight points from Stephen Jones had kept the Lions' noses in front before Joe Pietersen's late try threatened to bring an end to their fine start to the 10-match tour.
Fortunately for the tourists, the previously reliable Willem de Waal failed with his conversion attempt to leave the scores tied at 23-23 with 64 minutes on the clock.
The remaining quarter of an hour proved to be a nervy affair, but the Lions kept their composure to ensure the momentum continues to build towards the three-game series with the reigning world champions.
Dominance in the scrum played a key role in proceedings, particularly in the latter stages when the Lions could easily have let victory slip from their grasp, while Hook deserves great credit for somehow firing the Lions to victory from close to 50-metres despite the presence of a swirling wind.
Cape Town is renowned for its erratic weather conditions and the driving rain and unpredictable breeze certainly didn't prove conducive to attractive, running rugby yet the Lions still managed to claim three scores of the highest order.
The majority of the opening half was dominated by the boot, with two Jones penalties being superseded by a penalty and a drop goal from de Waal and a further drop from full back Pietersen.
The result was a three-point advantage to the home side after 27 minutes before two superb tries turned the game in the Lions' favour.
Bowe was heavily involved in both efforts, somehow escaping the clutches of Pietersen to cross for the first on 28 minutes before slicing through the Western Province defence to set up wing partner Monye for the second seven minutes later.
Andy Powell confidently claimed a high ball on his own 10-metre line wide on the left before charging through the opposition and taking play back towards centre field. Rather than going to ground, as he had done predominantly during the win over the Cheetahs, the Wales No8 kept the ball alive with a deft offload to countryman Williams.
The Lions openside performed his traditional link role perfectly, taking the ball from Powell, turning his back into the onrushing defence and feeding scrum-half Harry Ellis to keep the visitors well and truly on the front foot.
Ellis moved possession wide, Keith Earls provided a decoy run and Rob Kearney supplied the scoring pass.
Bowe still had plenty to do but, just as he had done in the opening two matches on tour, the Ospreys star made light work of what was in front of him. Three Western Province defenders were unable to bring Bowe to ground as he span out of one tackle and ran straight through two more before forcing the ball down five metres in from the right-hand touchline.
Jones was off-target with the attempted extras but he made no mistake from an identical position on the opposite side of the pitch following Monye's 35th-minute score.
This time, Bowe turned creator, taking Jones' pass behind the first line of attackers on halfway and gliding between the Western Province midfield before producing a brilliant offload that set Monye free.
Bowe's floated five-metre pass allowed Monye to continue at full speed and the Quins wing showed his growing maturity with a diving finish that made the most of the wet ground and ensured the covering defence would be unable to drag him into touch.
Jones' well-taken conversion gave the Lions a nine-point advantage and, with the way in which they finished the games against the Sharks and the Golden Lions, it looked as though they may run away with proceedings now that they had finally established some breathing space.
It wasn't to be, however, as Western Province showed the same kind of character displayed by the Sharks for 40 minutes on Wednesday for a full 80 this afternoon.
Penalties either side of half-time from de Waal immediately cut the deficit to just three points and, although a Williams try again hinted at what might have been for the Lions, Western Province refused to give up the fight.
Whereas the tries from Bowe and Monye had come from quick ball and expert finishing out wide, showing what the Lions are capable of when space opens up in front of them, Williams' effort was a far more conservative, yet equally impressive score.
Forward power allowed the Lions to recycle passion repeatedly inside the Western Province 22, with the squad collective preventing anyone player from breaking off without the support of his team-mates.
Patience was the key as the Lions continued to drive forward and Williams was the man to spot the gap when it finally opened up. The veteran flanker marked his return from a shoulder injury with a timely reminder of his abilities and it was he who broke off the back of a maul as it descended into another ruck four metres shy of the opposition line.
Williams spotted scrum-half Dewaldt Duvenage defending the narrow blindside and simply barged his way through his more lightweight opponent to send the Lions eight points clear with 25 minutes left to play.
Jones failed with the attempted conversion from wide on the left but it again appeared as though the Lions may have received the boost they needed to move on and control the remainder of the match.
The Lions failed to build on that advantage, though, as a fourth penalty from de Waal brought the home side back to within a single score.
That score was then supplied by Pietersen, following a strong burst from second row Anton Van Zyl and suddenly the Lions were in real danger of falling to a shock defeat.
Momentum was back with the South African side and the Newlands crowd sensed a first victory over the Lions since 1938. The Lions could easily have folded and therefore suffered a major setback prior to Saturday's clash with the Boks but instead they stuck to their task and finished the stronger of the two sides.
Just as they had done against both the Cheetahs and the Royal XV earlier in the tour, the Lions stayed focused under pressure and were rewarded for that composure when they were given a brace of penalties in the closing stages.
Hook missed with the first of those attempts just three minutes after coming on following Pietersen's try but the 23-year-old made no mistake with the second to secure another valuable victory for the Lions.
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