But AC Milan regrouped, and a goal from Alessio Romagnoli gave them a lifeline.
The highly-intense historical Milan derby 2017 is set to be contested in the morning, possibly for the first-time ever.
Pressure has been mounting on Pioli, while the mood in the Milan camp has been one of positivity following six victories in their last nine and the long-awaited completion of the €740million takeover by Chinese investors this week.
AC Milan's general manager Marco Fassone, meanwhile, has also revealed that the Chinese owners look keen on building a new stadium. I think it was a great game to watch for our fans.
AC Milan have a slight edge over Inter Milan in Serie A right now, with the Rossoneri in fifth, two points above their great rivals.
"Our first half hour was good, we created chances, but we weren't clinical enough".
Deulofeu struck the base of the post with a low strike from the right of the area but Inter threatened straight away on the counter-attack in a breathless opening 20 minutes.
Kin Club Easter Egg Hunt back for 37th year
The popular holiday tradition will include a search for a special gift-filled egg in the store's nursery department. After collecting their eight egg limit, children stood in line with their families to trade their eggs for prizes.
Inter and AC Milan have conceded the joint-fewest headed goals so far in Serie A this season (three apiece).
Incredibly, they made it count, with Manuel Locatelli flicking Deulofeu's corner into the path of Zapata, who drove the ball over the line - via the cross bar - despite the best efforts of Gary Medel. 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.
Montella urged his men up the pitch and with seven minutes remaining Romagnoli launched the fightback with a volley from Suso's cross that beat Handanovic.
Goal-line tech confirmed it, and here is the image below of the ball over the line. It was Icardi's 21st league goal of the season and perhaps more significantly, his first in the Milan Derby.
While that might not be taking shape anytime soon, let us get our attention back on the Derby di Milano, or the Milan Derby on Saturday.
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.