Alessio Romagnoli prodded in eight minutes from time to give Rossoneri hope of a comeback before Zapata pounced on a Manuel Locatelli header to volley home in the seventh minute of stoppage time and claim an unlikely point.
"In the first game I saw them cheer, this time I celebrated more than I usually do, I now understand the joy the Inter players felt in the first game".
The match is booked as a "home" game for Inter Milan but AC Milan could find themselves in some kind of a renewed vigour after a new era started for the club on Friday, with Chinese investment firm Rossoneri Sport Investment Lux completing a £628m takeover of the club, taking the mantle from former Italy Prime Minister Silvio Berlusconi. I think it was a great game to watch for our fans.
The arch-rivals remain where they were in the league table, with Milan in sixth place with 58 points and Inter in seventh, two points behind.
Deulofeu went close again in the 14th but his effort went off the base of the right post from a tight angle. Gagliardini's simple long ball from halfway allowed Candreva to run in behind Mattia De Sciglio and loop a clever finish over Gianluigi Donnarumma and into the bottom-left corner.
Inter and AC Milan have conceded the joint-fewest headed goals so far in Serie A this season (three apiece).
It hit the underside of the crossbar and was hooked away by Gary Medel but the referee, aided by goalline technology, signalled that the ball had crossed the line, prompting wild celebrations among the Milan players. "The others are good too, and we need to work harder". Ivan Perisic combined well with Joao Mario down the left and drilled a low cross into the path of Icardi, who fired into the gaping goal from six yards.
Daniele De Rossi nearly scored a spectacular goal but his overhead kick from the edge of the area crashed off the post.
But it was Inter who drew first blood with their first goal before half-time in a derby match since Walter Samuel in 2012.
However, Juventus forward Paulo Dybala limped off in the 54th with an ankle injury, which will be a worry for the Bianconeri ahead of the second leg of their Champions League quarterfinal, where they lead Barcelona 3-0.
Little changed at the bottom of the table after Palermo picked up a point in a 0-0 draw with Bologna, Crotone held Torino 1-1, and Empoli earned a 1-1 draw at Fiorentina which maintained their four-point gap above the drop zone.