Jonny Wilkinson posted 13 points with the boot but the Lions made life difficult for themselves by failing to turn their first-half domination into a convincing advantage.
Sir Clive Woodward fielded a Test-strength side as they looked to put their tour back on track after Saturday's loss to the Maori.
England World Cup stars Wilkinson, Jason Robinson and Neil Back were among a handful of players making first tour starts.
Skipper Brian O'Driscoll and full-back Josh Lewsey featured for the third time in four games, Gavin Henson also started, and flanker Simon Easterby was handed a Lions bow.
Wilkinson's appearance created a buzz of anticipation, yet he will be looking to kick with a higher accuracy percentage in later games.
Wellington's All Blacks Tana Umaga, Jerry Collins, Rodney So'oialo and Conrad Smith were all unavailable to coach John Plumtree.
Conditions were breezy as O'Driscoll led the Lions out.
Wilkinson drifted a drop-goal attempt from 25 yards wide of the posts inside 30 seconds. Henson then did likewise.
Wilkinson made no mistake with an eighth-minute penalty attempt, though, following more livewire work by Shane Byrne.
Byrne's fellow Irishman Easterby showed up well during the early exchanges, but the Lions had territorial dominance and should have scored more points.
Wilkinson fired a 16th-minute penalty wide but his second penalty in the 24th minute moved the Lions 6-0 up.
Despite some brief threats from their All Blacks centre Ma'a Nonu, the home side had barely featured, but they scored when it mattered.
Nonu won a penalty which fly-half Jimmy Gopperth fired between the posts.
Martin Corry came within inches of touching down with a great opportunity for the Lions, and Ben Kay made a handling error when trying to gather the loose ball.
While rain swept in, the Lions only had themselves to blame for not being further ahead.
But then came a Lions try, started and finished by two Welsh Grand Slam stars.
Scrum-half Dwayne Peel ghosted into space and, after Corry acted as an intelligent link, prop Gethin Jenkins took Corry's pass and sprinted 15 metres to score, with Wilkinson landing the touchline conversion.
Gopperth struck his second penalty, narrowing the deficit to 13-6 at half-time.
Wilkinson kicked a third penalty in the 44th minute, before Nonu went close for Wellington following a robust touchline charge.
Henson was replaced by fellow Welshman Stephen Jones, with Wilkinson moving to inside centre to accommodate the fly-half.
Robinson also switched positions, taking up full-back duties when Shane Horgan replaced Josh Lewsey.
Wellington clung onto the 10-point deficit as the closing stages approached, but the try the Lions had been pressing for finally arrived three minutes from time, when Thomas stole possession and burst clear for a kick-and-chase score that Wilkinson converted.
The Lions now head south to Dunedin for Saturday's appointment with Otago.