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 thumping victory on home soil
Lionel Messi was the history-making hero, becoming the first player to score five times in a single Champions League match.
The Catalan giants entered the night with a 3-1 aggregate advantage from the first leg, and Messi's exploits, plus a double from tournament debutant Cristian Tello meant that Karim Bellarabi's late goal was only a consolation strike as Barca advanced by a 10-2 aggregate margin.
The hosts had control 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, but 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 beautifully 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 minute, 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 half-time.
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 interval, Messi completed his hat-trick with another phenomenal effort. After receiving Cesc's ball over the top, the 24-year-old created just enough space to fire at goal, and again chipped his shot, leaving Leno with no chance.
Tello joined the fray as a substitute on 55 minutes, and within seconds found himself at the end of Cesc's flick, striking low into the net.
The 20-year-old made it two for him in the 62nd minute as he received the ball in a similar position, and again beat Leno with a low strike that squirmed under the custodian.
Between Tello's strikes, Messi grabbed a fourth. 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 byeline before striking inches wide from a tight angle.
After the hour mark, things quieted as Barca rested on their lead, while Leverkusen offered little resistance as the hosts dominated possession. Five minutes from full time, 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 a single match in Europe's elite competition, and took his Champions League account for the season to 12 goals in just 7 outings.
Leverkusen would 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 the demoralised away side, 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 at the hands of an elite side. In progressing, the hosts have reached the quarter-finals for the fifth consecutive season, and now wait patiently for the draw, which takes place on March 16.