Saturday's result enabled the Gunners to keep up with Premier League leaders Chelsea.
Laurent Koscielny bundled home his first Arsenal goal on 24 minutes, only for the French defender's poor back header to allow Bolton to equalise just before half-time through Johan Elmander.
Marouane Chamakh headed the hosts back in front, with Gary Cahill then sent off for a tackle from behind on the Moroccan.
Alex Song netted Arsenal's 1,000th Premier League goal under manager Arsene Wenger and substitute Carlos Vela stroked in number four with seven minutes left.
The unbeaten Gunners have now won three of their opening four league games, making the most of rivals Manchester United dropping points at Everton while also making sure Chelsea, with a 100% record, are still within touching distance.
"We have had two games, at Blackburn and today, which we certainly would not have taken six points from two years ago," Wenger said.
"The players can handle these situations.
"Overall it was a competitive game where we dominated and created many chances, but when you play against Bolton, as long as you don't kill the game off, they can score - you can dominate 80% of the game and still lose.
"They marked us very tight, which provoked a very physical game, but they also played well.
"Bolton had full commitment and we needed to be patient, to get our technique and passing to prevail.
"It was a good test for our two centre-backs, who did very well and I am pleased with the performance of the whole team."
Referee Stuart Attwell deemed Cahill's challenge from behind worthy of a straight red, but also let some other hefty challenges go unpunished - most notably Paul Robinson on Arsenal substitute Abou Diaby, who latter hobbled off.
Wenger reflected: "There could have been other red cards.
"You have to see it again because in the heat of the game it is sometimes difficult to judge, but the challenge on Diaby was a bad tackle.
"He is not in a very good shape. Diaby cannot move his leg at the moment, so we will see how we get away with it."
Captain Cesc Fabregas was in fine form at the heart of the Arsenal side, now looking fully match fit following his break after the World Cup and very much committed to the Gunners cause following a summer of speculation over a move to boyhood club Barcelona.
"I was always convinced he loved Arsenal as well and that he loves to play football. When he is on the pitch, he enjoys it," Wenger said.
"We play the game he loves to play, the game turns around him as well.
"He grew up in this team, and to make this team win will be a bigger achievement than anything else for Fabregas."
Bolton manager Owen Coyle lamented the decision of Attwell not to award what looked like a trip by Kieran Gibbs on Lee Chung-yong in the build-up to the Arsenal breakaway which resulted in Cahill's dismissal.
"Lee was very close to the penalty box. It should have been a free-kick, and it is not given," said Coyle.
"From the resulting pass, Gary Cahill went into the back of the lad and fouled him. I don't think it merited a red.
"All of a sudden we were playing Arsenal with 10 men, and it is difficult at the best of times with 11.
"We had put so much into the game that at that time we looked like the team who would get the equaliser."
Coyle added: "As managers, we have to watch what we say for fear of getting into trouble and if I was to elaborate on it, I would be in trouble because it was a huge turning point in the game.
"I don't want people booked, all I ask is that when my team plays we are treated in the same way as the opposition and I don't feel we were today.
"The little bitty fouls can go either way and we accept that, but this was a clear free-kick."
Bolton goalkeeper Adam Bogdan impressed on his first Premier League start in place of the suspended Jussi Jaaskelainen, as the Hungarian made a string of fine saves.
"We have got great belief in Bogdan. That's why we played him," said Coyle.
"He is improving no end and was unlucky to concede four goals today given his level of performance."