The defending German and European champions will take a healthy advantage into their home leg of the last 16 tie, but such comfort appeared unlikely as Arsenal tore into their illustrious visitors during the opening exchanges on Wednesday.
Crucially, playmaker Mesut Ozil saw a tame ninth-minute penalty saved by his international team-mate Manuel Neuer and the game then turned decisively on another penalty decision.
Neuer's opposite number Wojciech Szczesny was sent off for a professional foul on Arjen Robben with 37 minutes played and, although David Alaba subsequently failed to convert from 12 yards, Arsenal were left facing an uphill task.
Despite a brave display from the hosts, the outstanding Toni Kroos and substitute Thomas Muller gave Guardiola's team the advantage their continued second-half pressure merited.
"They were much, much, much better than us in the first 10 or 15 minutes," former Barcelona boss Guardiola told Sky Sports.
"After the mistake by Ozil the game was more equal. From that moment we played better and after the red card for the goalkeeper it was another game.
"It's difficult to play when you see nine players in the box (defending), it is not easy. You can attack with nine players but it is not easy, never.
"But we played with patience and at the end we found the (second) goal.
"The last two times I came here with Barcelona and we played amazing and didn't win. So I know how difficult it is to win here. I accept we played 10 against 11 so it is easier in that point.
"If we think about defending our result we will be eliminated by Arsenal. If we play to win the game maybe we are going to the quarter-finals."
Neuer, meanwhile, revealed his familiarity with Ozil's nonchalant penalty style proved to be the Arsenal player's downfall.
"I know how Mesut Ozil takes penalties," he said.
"I knew he would wait a long time before deciding in which corner to shoot but, of course, he could have picked any corner."
Neuer added: "We still know the knockout phase is all about getting through over two legs. There is still a lot that could go wrong."
