With second-placed Roma only drawing 0-0 at Empoli, Milan moved to within one point of them and five behind leaders Juventus, who beat Napoli on Saturday.
"It was a precious victory against a very tough opponent," coach Vincenzo Montella told the club's website.
"We should have been more clinical and put the match to bed earlier, but I am pleased with the team's spirit, so well done to the boys."
It was hardly a convincing performance from Montella's side, though, and struggling Pescara kept Milan's precociously talented keeper Gianluigi Donnarumma busy before and after falling behind.
Donnarumma made a superb double save to deny Ledian Memushaj while Pescara, without a win in eight league games before Sunday, twice had the ball in the net only to have their celebrations cut short by offside flags.
Carlos Bacca did hit the woodwork in the second half for Milan but the hosts were relieved to hear the final whistle.
"We didn't start that well. We didn't take advantage of spaces, but then we improved and dominated the game," Montella, whose team travel to Palermo next week, said.
Empoli have scored only two goals in 11 Serie A games this season but defended resolutely to frustrate Roma who had been expecting a fifth consecutive league win.
Lazio also climbed above Napoli into fourth spot after goals from Senad Lulic and Ciro Immobile earned them a 2-1 win over Sassuolo.
Inter Milan slumped to their fourth defeat in five league games, going down 1-0 at Sampdoria in Sunday's late game.
Fabio Quagliarella's goal just before halftime settled the contest, sending Sampdoria level on points with 11th placed Inter.
Bottom club Crotone won their first match of the season, beating Chievo Verona 2-0.
(Reporting by Martyn Herman; Editing by Ian Chadband)
