With the return leg at the Nou Camp on March 7, Barcelona dominated possession in this David versus Goliath clash against a Leverkusen who have now won just one of their last eight games. The winner will go through to the quarter-finals.
For all their super-star status, Barcelona, who lag ten points behind leaders Real Madrid in the Spanish league, stumbled at times and Leverkusen squandered chances to earn a draw.
"I think the second half was good, we used the space better after we took the lead," said Barcelona coach Pep Guardiola. "We tried to improve our game, we had a few chances in the first half, but perhaps the final pass was missing.
"But we were playing away and we came into the game after the break."
Nevertheless, Barcelona are in pole-position to reach the last eight after two goals by Chile's Alexis Sanchez and a late strike by Lionel Messi gave them a valuable away win while Leverkusen defender Michal Kadlec grabbed a consolation.
"The defence was good in the first half, but we were lacking a bit of courage," said Leverkusen coach Robin Dutt. "We gave them too much respect and were a bit anxious. It was a completely different story in the second half when we played our
part in the game and caused Barcelona some problems."
Barcelona boasted a midfield of World Cup winners Andres Iniesta, Sergio Busquets and Cesc Fabregas behind a forward line containing Brazil's Adriano, Sanchez and three-time world footballer of the year Messi.
The injury-enforced absences of midfielder Sidney Sam and Swiss striker Eren Derdiyok were a major blow to the hosts, while ex-Germany captain Michael Ballack was ruled out on Sunday with a calf injury.
On a cold night at the BayArena, the Catalan side took most of the first-half to warm up with Messi showing only rare flashes of skill early on.
With Barcelona enjoying around 80 percent of the possession, it was a matter of time before the hosts' defence cracked.
A through ball from Messi saw Dani Alves and Sanchez sprint head-to-head after the ball and it was the Chilean who arrived first to fire past Leverkusen goalkeeper Bernd Leno on 41 minutes.
Barcelona's half-time lead was harsh on the hard-working hosts, but with virtually their first full attack of the game, Leverkusen equalised.
Former Tottenham Hotspur defender Vedran Corluka managed to chip in a cross and Czech Republic defender Kadlec headed home at the back post for a goal which had the 30,000-capacity crowd on their feet on 52 minutes.
Barcelona, however, needed just three minutes to pull ahead again when Sanchez added his second after a ball from Fabregas allowed the Chilean to round Leno and fire home.
Leverkusen came out fighting and Renato Augusto forced Barcelona goalkeeper Victor Valdes into a save moments later, while midfielder Gonzalo Castro hit the post on 64 minutes with Valdes beaten.
Despite a posse of defenders shadowing his every move, Messi hit the post with 72 minutes gone, but at the other end striker Stefan Kiessling came on with 15 minutes left and headed at Valdes with his first touch of the game.
Messi saved the best for last when he finished a great cross from Alves for the third on 88 minutes.