Roger Schmidt's side left the Camp Nou empty-handed despite dominating and leading for long periods. Meanwhile, Bayern Munich stormed past Dinamo Zagreb who suffered at the hands of Robert Lewandowski.
Barcelona 2-1 Bayer Leverkusen
(Roberto 79', Suarez 81' - Papadopoulos 22')
Luis Suarez's 81st minute goal capped off the perfect turnaround for last season's Champions League winners Barcelona who narrowly avoided their first group stage defeat since 2009 against Bayer Leverkusen.
Suarez scored his 31st goal in European competitions, a strike which takes him beyond Edison Cavani as the highest-scoring Uruguayan in continental tournaments. He netted 92 seconds after Sergi Roberto squeezed home the equalizer to cancel out the opener from Kyriakos Papadopoulos.
Peerless defensive performances from Papadopoulos, Jonathan Tah and Lars Bender inspired Leverkusen to the brink of their most impressive Champions League win since they reached the final in 2002. But the Camp Nou continues to be a smudge on their European record after the 7-1 defeat last time out.
The Catalans last went down in the group stages against Russian cracks Rubin Kazan in 2009; whilst the hysteria surrounding the absence of Lionel Messi seemed ominous. The Argentine was ruled out for several weeks with a knee injury, which was sustained in the win over Las Palmas at the weekend. Luis Enrique dipped into the La Masia talent pool and handed Sandro Ramirez a rare start in attack alongside Neymar and Luis Suarez.
But the 20-year-old was ineffective and the side struggled without the all-encompassing qualities of Messi. Leverkusen started sharply, pressing high up the pitch and creating chances of their own straight from the first whistle. After 67 seconds, Javier Hernandez, who scored on matchday one against BATE Borisov, missed his first clear chance of the evening.
On 19 minutes, the tenacity of midfielder Kevin Kampl was rewarded in two golden chances. The former Borussia Dortmund player was brilliant in pressing, but hesitant in front of goal and wasted the best openings of the game. Kampl's blushes were spared three minutes later. Hakan Calhanoglu's corner kick, swung on top of Marc-Andre ter Stegen was flicked into the net by Greek defender Papadopoulos. The center-back then showed his value in last-ditch defending, clearing heroically off the line from Neymar's goal bound shot on 39 minutes.
Leverkusen should have wrapped up the points on 49 minutes, a chance squandered by Hernandez. The Mexican striker was played in by Karim Bellarabi and completely miskewed his shot, the ball missing the target from about 15 yards out. As Schmidt's players ran out of gas, Barca started to pile on the pressure. Ivan Rakitic shot wide on 56 minutes, while Neymar's free kick was inches past the post after the hour mark.
And on 79 minutes, Leno couldn't hold on to a shot from Neymar and Roberto sprinted to level. Before Leverkusen had time to settle, Suarez controlled on the edge of the box, thumping in a superb finish to leave Roger Schmidt's men returning home pointless from this European adventure.
Bayern Munich 5-0 Dinamo Zagreb
(Costa 13', Lewandowski 21', 28', 55', Götze 24')
Robert Lewandowski scored his second hat trick in three games as Bayern Munich demolished Croatian champions Dinamo Zagreb 5-0.
With 10 goals in his last three games, Lewandowski blistering form takes him level with Mario Gomez on 26 Champions League goals, ending Dinamo Zagreb's impressive 45-game unbeaten run. "He's had an unbelievable week," noted Philipp Lahm after the final whistle.
The German champions were ahead after 13 minutes with Douglas Costa squeezing the ball past Eduardo at the front post. Bayern have developed a habit for quick fire scoring streaks and they would net another three goals inside seven minutes.
First, Lewandowski finished off a great piece of individual play from Thiago Alcantara. Three minutes later, Mario Götze drifted in from the right-flank and scored for the second matchday running in the Champions League. On 27 minutes, Costa's pace on the wing proved too much for Zagreb right-back Alexandru Matel, his cross clipped into the net by Lewandowski.
"Football is all about attitude," insisted Matthias Sammer pre-match. The Bayern sporting director warned his men about the danger of underestimating Croatian champions Dinamo Zagreb - but there was little need to be concerned. Croatia's current league-leaders were tame in attack and rarely threatened Manuel Neuer's goal.
Ten minutes after the break, Bayern netted a fifth for the night, the in form Polish striker capping off a wonderful move which involved Costa and Thiago around the edge of the box. With two assists, Thiago looked finally back to his best in a more advanced midfield role, helped by the maturity of Joshua Kimmich and the eventual introduction of Javi Martinez.
Bayern's group rivals Arsenal - their next opponents on matchday three in London - went down 3-2 at home to Olympiacos, leaving the Bavarians clear at the top of the section. Bayern has won 10 games from 10 in all competitions this season and is now looking ahead to the visit of Borussia Dortmund on Sunday.
Champions League matchday two results:
Bayern Munich 5-0 Dinamo Zagreb
Arsenal 2-3 Olympiacos
Barcelona 2-1 Leverkusen
BATE Borisov 3-1 Roma
Porto 2-1 Chelsea
Lyon 0-1 Valencia
Maccabi Tel-Aviv 0-2 Dynamo Kyiv
Zenit 2-1 Gent