The holders sealed progression to the last eight of Europe's elite competition on Wednesday as they followed up their 3-1 first-leg win with a victory on home soil.
The Catalan giants entered the night with a 3-1 aggregate advantage from the first leg, and five goals from the spectacular Lionel Messi, plus a double from Champions League debutant Cristian Tello, meant that Karim Bellarabi's late goal was only a consolation strike as Barca advanced by a 10-2 aggregate margin.
Messi became the first player to score five in a Champions League game. It was also the first time Barca scored seven goals in a UCL match.
Barca had control of the match from the early stages of the match, and Messi nearly put his side ahead after 11 minutes after being played into the box by Cesc Fabregas. Bernd Leno did very well to push the Argentine's shot around the post.
Xavi was next to threaten, with free kicks on 13 and 24 minutes causing trouble, but the former narrowly missed the target, while the latter was again parried by Leno.
Leverkusen's fortunes eventually turned, and on 25 minutes, Messi latched onto Xavi's chipped ball before lifting his finish over the goalkeeper and into the net.
Barca pushed on for more, and Messi cut in from the right after a half-hour before having his shot blocked. In the 42nd minutes, the scorer tried a similar move, but this time had space to fire an unstoppable finish into the lower-left corner, doubling the hosts' advantage and putting the tie beyond any doubt before halftime.
The hosts nearly got a third before the break, but Leno was quick off his line to deny Fabregas, and moments later, Pedro.
Five minutes after the break, Messi completed his hat trick with another phenomenal finish. After receiving Fabregas' ball over the top, the 24-year-old created just enough space to shoot, and again chipped his finish, leaving Leno with no chance.
Tello joined the fray as a substitute on 55 minutes, and within seconds found himself at the end of Fabregas' flick, striking a low strike into the net.
The 20-year-old made it two goals in one game in the 62nd minute as he received the ball in a similar position, and again beat Leno with a low strike.
Between Tello's strikes, Messi grabbed a fourth, making him the first player in history to scour four goals in two separate Champions League games during his career. The Ballon d'Or winner was initially stopped, but after Leno spilled the ball, he tapped home from close range.
Before the final exchanges, Leverkusen's only meaningful attempt came after the tie was already decided, in the 54th minute when Eren Derdiyok beat Javier Mascherano to the end line before striking inches wide from a tight angle.
After the hour mark, things quieted as Barca rested on its lead, while Leverkusen offered little resistance as the hosts dominated possession. Five minutes from fulltime, however, Messi scored a brilliant fifth, bending his strike from the edge of the box just inside the left post.
The Argentine's tally was the greatest ever for a player in Europe's elite competition, and raised his count to 48 strikes in 42 games.
Leverkusen would get a strike at the death as Bellarabi played a one-two with Simon Rolfes before striking a hard finish to the far post, but it was little consolation for Leverkusen, whose defeat equalled the worst-ever result for a team in one leg in the round of 16.
In the end, Leverkusen proved no match for Barcelona, and crashed out of Europe's greatest club competition at the hands of an elite side. In progressing, the hosts have reached the quarterfinals for the fifth consecutive season, where they fill face a to-be-announced team that will be revealed on Friday, March 16.