Pulisic struck with three minutes remaining when he spun and slammed home the goal which was only given after a long VAR check for a possible handball while the USA star controlled the ball.
The 25-year-old's fourth goal since signing for Milan in the summer moved his team two points ahead of Inter, some revenge for the five-goal humiliation suffered in last month's derby.
Saturday's narrow win against a spirited Genoa missing Italy forward Mateo Retegui was Milan's fourth in a row in Italy's top flight since being thumped by Inter.
It came following a largely stodgy contest at the Stadio Luigi Ferraris which came alive in the final minutes and finished with both teams down to 10 in the most unlikely of fashions.
Mike Maignan was dismissed in stoppage time for charging out of his goal and clattering into Caleb Ekuban, meaning that Milan will be without him and his France teammate Theo Hernandez against Juventus next week and had to have Olivier Giroud in goal for the final seconds.
Giroud had to immediately face down a free-kick which Albert Gudmundsson clipped onto the crossbar.
Then moments later, after Genoa's Josep Martinez was shown a second yellow card while charging back to his own goal from the subsequent corner, Giroud produced an unorthodox double save to make sure Milan took the three points back to the San Siro.
Juve's derby delight
Juventus are four points behind Milan in third after their 2-0 derby victory over struggling Torino.
Second-half goals from Federico Gatti and substitute Arkadiusz Milik made sure Juve stayed within sight of Milan and moved three in front of fourth-placed Napoli ahead of the champions' home clash with Fiorentina on Sunday.
"We're not looking at what other teams are doing, we just want to win every game that we play, that's the only way to the top... there's a very long way to go," said Milik.
Juve's win came without starting centre-forwards Federico Chiesa and Dusan Vlahovic, both out injured for the match at the Allianz Stadium in Turin.
Chiesa risks missing out on Italy's two Euro 2024 qualifiers with Malta and England but was selected in the Azzurri squad by coach Luciano Spalletti on Friday.
Ivan Juric's team were also missing a clutch of players and never looked like ending their dismal record in derbies with Juve, last beating Italy's biggest-supported club back in April 2015.
They drop down to 12th after a third straight match without scoring, their fourth without a win.
'Angry' Inzaghi
Simone Inzaghi's Inter looked set to ensure top spot in Italy until after the international break when Francesco Acerbi and Lautaro Martinez gave the hosts a commanding lead in the first 13 minutes at the San Siro.
But a Riccardo Orsolini penalty six minutes later and Joshua Zirkzee's fine finish shortly after half-time snatched a draw for Bologna.
"I'm angry just as the players are in the dressing room," said Inzaghi to DAZN.
"It's the second time, after Sassuolo (a 2-1 defeat), that we lead and don't win because of mistakes and lack of attention which have cost us dearly.
"We should have scored more than two goals in the first half."
The one positive for Inter was the continued superb form of Argentina forward Martinez, who took his league tally to 10 in eight matches with his rocket of a strike.
