PHOTO: AFP
Samu Castillejo nodded Milan ahead after 69 minutes but Alves pulled the sides level with a curling free-kick three minutes from time.
AC Milan remain fourth on 56 points but Roma are two points behind in fifth before they play third-placed Inter Milan at the San Siro later on Saturday.
Atalanta, sixth, can pull level with Milan on points when they travel to second-placed Napoli on Monday.
Lazio are also lurking four points behind ahead of their game against relegated Chievo on Saturday with Torino seven points adrift of the Champions League places before travelling to Genoa.
Castillejo came off the bench after 66 minutes and had an immediate impact when he headed in a Suso cross three minutes later.
Patrick Cutrone had a goal ruled out for offside minutes later but Alves snatched a point for promoted Parma with a free kick that left returning Milan goalkeeper Gianluigi Donnarumma helpless.
Parma move up to 13th place, seven points above the relegation zone with five games left.
"It wasn't a great performance," said Milan coach Gennaro Gattuso.
"I expected to come here and do more. Parma made the most of that free kick with a wonderful goal. They deserved the point."
Champions Juventus can seal an eighth consecutive Serie A title later on Saturday, with the Turin giants needing just a point against Fiorentina for their 35th Scudetto.
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