Donnarumma pulled off one of the saves of the season to earn Milan a point against Napoli in their last outing, but the youngster was in no man's land when Lorenzo De Silvestri cancelled out Milan's lead on 70 minutes.
Giacomo Bonaventura's stunning ninth-minute strike had put the Rossoneri ahead against the run of play - Andrea Belotti having failed to convert from the spot early on.
Buoyed by the return of Leonardo Bonucci, Milan's defence were in fine form for much of Tuesday's clash, although Donnarumma was called into action to deny Belotti before Iago Falque squandered a gilt-edged chance as Torino pressed for a first-half equaliser.
Torino looked devoid of ideas for much of the second half, but Donnarumma's failure to claim Adem Ljajic's inswinging corner allowed De Silvestri - who saw red in stoppage time - to head home the equaliser.
Torino were gifted an opportunity to go ahead inside three minutes when Franck Kessie bundled into Cristian Ansaldi, only for Belotti to hammer the resulting spot-kick against the woodwork.
Milan wasted no time in making Torino pay - Bonaventura despatching an exquisite half-volley up and over Salvatore Sirigu.
Donnarumma was Milan's hero last time out, and the youngster was at his best again to tip over Belotti's looping header on the half hour.
Falque was presented with a great opportunity from the resulting corner, only to shank his effort over after latching onto Ansaldi's cross.
Kalinic should have extended Milan's lead before the interval, but the striker's dire form in front of goal continued as he headed wide from six yards out.
Former Fiorentina striker Kalinic turned provider after the interval with a neat pass into Fabio Borini, only for the forward to nudge the ball straight into the hands of Sirigu.
Torino's goalkeeper was called into action again on the hour, but was not challenged by Suso's tame long-range effort.
Ansaldi was enjoying a fine game down Torino's left, and went close to marking his performance with a terrific goal with a venomous strike that whistled just over.
Torino did have their equaliser soon after, though - De Silvestri beating Donnarumma to Ljajic's wicked delivery and duly converting from close range.
Milan's goalkeeper atoned somewhat in the closing stages however, lunging to his left to tip another Ljajic effort wide.
And there was to be more drama in stoppage time - De Silvestri receiving a second booking for a high tackle on Ricardo Rodriguez before Abate struck the woodwork with a long-range effort as both sides ultimately settled for a share of the spoils.
Key Opta Facts:
- AC Milan have drawn four Serie A games in a row in a single season for the first time since April 1994.
- Milan have scored seven goals in the opening 10 minutes of play, the joint-most in this Serie A campaign (along with Fiorentina).
- Andrea Belotti has failed to score five of his last seven penalties taken in Serie A (six out of 13 in total in the top-flight).
- Adem Ljajic has provided eight assists in Serie A this season (his joint-best tally in a single campaign); the last five came from set-pieces.