AC Milan's Thiago Silva headed in late on to seal a 2-2 draw against Barcelona at the Nou Camp.
Pato's goal after 24 seconds had put the Italian side ahead before Pedro Rodriguez (36 minutes) and David Villa (50) gave Barcelona a 2-1 lead.
Elsewhere, Porto defeated Shakhtar Donetsk 2-1 and Marseille won 1-0 at Olympiakos.
Newcomers Viktoria Plzen earned their first point with a 1-1 home draw against BATE Borisov.
Pato had exposed Barcelona's defensive frailties to score the fifth fastest Champions League goal ever, bursting through before finishing through Victor Valdes's legs.
Lionel Messi was instrumental in many of Barcelona's best moves as they tried to recover and the Argentina forward embarked on a dangerous run and then cut the ball back for Pedro Rodriguez to equalise.
And after 50 minutes, Villa appeared to have given them the win with a stunning 30-yard free-kick.
Milan snatched a point when Clarence Seedorf whipped in a corner and Silva outjumped Sergio Busquets before powering in. His goal was one of nine scored by Brazilians on the night.
Barcelona head coach Pep Guardiola said: "We did all we were supposed to do but we are still left with this bitter taste. We can admit that defensively we were not adequate. But I insist that we played a match that was more than adequate."
Milan manager Massimiliano Allegri said: "We got a little bit of luck but that's how football is. We didn't give up after going down 2-1."
Porto had to come from behind for a 2-1 home win over Shakhtar Donetsk, who were reduced to nine men. Hulk missed a 10th-minute penalty for Porto then, two minutes later, Luiz Adriano tapped in for Shakhtar. Hulk's 25-yard free-kick made it 1-1 just before the half-hour.
Shakhtar defender Yaroslav Rakitskiy was sent off for a studs-up challenge on Joao Moutinho close to half-time. Kleber poked in the 51st-minute winner before Dmytro Chygrynskiy was shown his second yellow card in the 80th minute.
Lucho Gonzalez scored in the 51st minute to ensure Marseille triumphed 1-0 at Olympiakos. The French team dominated most of the game at Karaiskaki Stadium, but created few scoring opportunities.
Marseille coach Didier Deschamps said: "It's a result that will give us calm and confidence. What was key for us was that we really wanted the win and went for it."
Newcomers Viktoria Plzen earned their first point with a 1-1 home draw against BATE Borisov. Striker Marek Bakos gave Plzen a 1-0 lead in first-half stoppage time, but Renan Bressan steered in a 69th-minute leveller. Plzen coach Pavel Vrba said: "I'm a little bit disappointed. BATE scored only due to our only mistake."
Cypriots Apoel Nicosia, making their second appearance in the competition, were up against Russian opposition for the first time and won 2-1 against visitors Zenit St Petersburg. Valencia, favourites with Chelsea to progress from Group E, drew 0-0 at Belgian side Genk.