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.
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."
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.
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."
"I think it is finished now," said former Manchester City and Tottenham Hotspur defender Corluka.
