Barca, who are now unbeaten in 13 Champions League games and have scored in 28 consecutive matches in the competition, are trying to lift the trophy for the third time in four years.
While Chile forward Alexis struck twice, it was Lionel Messi who once again stole the show with another sublime exhibition of ball skills capped by a late third goal from the World Player of the Year.
"We are very satisfied with the result because scoring three goals away is very important," said Barca coach Pep Guardiola.
The visitors grabbed the lead in the 41st minute after a brilliant left-footed flick by Messi sent Alexis racing through on goal.
Michal Kadlec equalised in the 52nd minute but the 23-year-old Chilean made it 2-1 three minutes later.
Messi completed the win, starting an 88th-minute move that also involved Dani Alves and finishing it with a volley at the far post as Barca avenged their 2001 defeat by Leverkusen, the last German club to beat them.
Asked whether he was planning to rest Messi, who has now scored a remarkable 25 goals in his last 24 Champions League matches, Guardiola replied: "Why? People want to see players like him.
"His life is football. He doesn't care. He's just happy when he plays. For us it's very important when he plays."
HARD WORK
Leverkusen, without injured playmaker Michael Ballack, knew they would have to work hard and chase the Spaniards for the ball and with 80 percent possession in the first half Barca set the tone.
The Germans managed to keep the scoring chances to a minimum until Messi lifted the ball over Leverkusen's back line and Alexis ran on to beat keeper Bernd Leno.
Leverkusen perked up in the second half and Kadlec gave them hope when he climbed high to head in at the far post after right back Vedran Corluka crossed from the by-line.
Alexis then scored from a tight angle after dribbling round Leno before Gonzalo Castro's low drive was expertly tipped on to the post by Barca goalkeeper Victor Valdes who followed up by stopping a diving header from Stefan Kiessling.
"Our defensive operation was good in the first half but we also had too much respect for Barca and were afraid," said Leverkusen coach Robin Dutt.
"In the second half it was completely different and we made it uncomfortable for them at times."
Leverkusen tried hard to force a second equaliser that would have kept the tie alive for the return leg in Spain on March 7 but Argentina forward Messi, who hit the woodwork earlier, put the game beyond the home team with two minutes left.
"I think it is finished now," said former Manchester City and Tottenham Hotspur defender Corluka.
