Pulisic combined with US teammate Yunus Musah to net the winner three minutes from time.
Fellow forward substitute Olivier Giroud also had a crucial part to play but in an unusual position.
The Frenchman's vital double save in the 14th minute of injury time came as he ended the match wearing the goalkeeper's gloves and jersey after Mike Maignan was sent off.
Milan had already used up all of their substitutes so Giroud took over in goal.
"I think I'm one of the tallest in the squad … so naturally I went in goal," said Giroud. "I liked going in goal when I was a kid too. But it was a really special emotion when I made the save, almost like a goal."
Milan will spend the international break solo at the top, two points clear of rivals Inter Milan, who let slip a two-goal lead to draw 2-2 at home to Bologna earlier on Saturday.
Juventus were third, four points behind Milan, following a 2-0 win over Torino in a derby match.
Milan coach Stefano Pioli opted to rest some of his players following Wednesday's 0-0 draw at Borussia Dortmund.
Milan's star attacking trident of Pulisic, Rafael Leão and Giroud started on the bench. Pulisic and Leão were brought on at halftime and Giroud came on in the 66th minute.
Pulisic roke the deadlock when he controlled Musah's cross with his back to goal and spun to drill the ball into the bottom right corner.
That was only the start of the crazy finale. Milan goalkeeper Maignan was shown a straight red card in the eighth minute of stoppage time following a collision with Genoa forward Caleb Ekuban.
Giroud assumed goalkeeping duties.
Albert Guðmundsson almost leveled from the resulting free kick as it was deflected off the crossbar and Fikayo Tomori then headed another attempt out for a corner.
Genoa goalkeeper Josep Martínez came up for that but ended up fouling a player and he was shown a yellow card and sent off too.
Genoa came close to snatching the equaliser with practically the last kick but Giroud showed bravery to rush off the line and save from George Pușcaș before desperately smothering the loose ball. He was surrounded and embraced by his teammates.
Inter seemed on course for victory when two goals in as many minutes from Francesco Acerbi and Lautaro Martínez gave them a 2-0 lead after 13 minutes.
Martínez's goal was a rocket into the back of the net but the Argentine World Cup winner helped Bologna to get back into the match in the 19th minute when he hauled down Lewis Ferguson in the area.
Riccardo Orsolini struck the resulting penalty into the bottom corner. That boosted Bologna, so soon after going 2-0 down, and Joshua Zirkzee scored the equaliser seven minutes into the second half.
Two corners led to two goals for Juventus.
Filip Kostić whipped in a corner from the right and Moise Kean's overhead kick was cleared off the line by Torino captain Ricardo Rodríguez, who also tried to do the same on Federico Gatti's follow-up. The ball appeared to have already crossed the line, however, but Gatti headed in the rebound to make sure.
The goal was originally disallowed for offside but was given on video review.
Juventus doubled their lead in the 62nd when Arkadiusz Milik headed in another Kostić corner from the right.
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