Inter had three goals ruled out and hit the post as many times in Sunday's match before De Vrij's stoppage-time equaliser cancelled out Tijjani Reijnders' first-half opener.
Second-placed Inter remained three points behind Napoli —-and with a game in hand - after the Serie A leaders conceded a stoppage-time goal to draw 1-1 at Roma.
Inter also had strong claims for a penalty turned down for a foul on Marcus Thuram in the second half.
"I can only compliment the team for how they overcame every obstacle this evening," Inter coach Simone Inzaghi said. "Three ruled-out goals, hitting the post three times and an obvious penalty not given."
Stefan de Vrij (l) celebrates his precious derby goal. (AP PHOTO)
Kyle Walker, who arrived recently on loan from Manchester City, was thrown straight into the starting lineup and he appeared to have a calming influence on the Milan defence - which had let in four goals in its past two matches.
Inter nevertheless had two goals disallowed for offside in the first half and also wasted several chances before being made to pay for its profligacy right on the stroke of halftime.
Theo Hernández sprinted downfield and sent a ball through to Rafael Leão, whose angled drive was parried by Yann Sommer but only as far as Reijnders to blast in the rebound from close range.
Inter had a third goal disallowed in the 64th minute for a foul on Hernández by Denzel Dumfries, who then crossed it for Lautaro Martinez to bundle in.
Yann Bisseck, Thuram and Dumfries hit the woodwork before Inter's siege finally paid off deep in added time as Nicola Zalewski chested down Bisseck's cross for De Vrij to sidefoot into the back of the net.
Just as Napoli thought they were about to go five points clear of Inter, Angeliño volleyed in a cross for the equaliser.
Napoli had led from the 29th minute following a rare goal from former Roma defender Leonardo Spinazzola.
France forward Randal Kolo Muani is rescuing Juventus - and perhaps saving coach Thiago Motta's job.
Kolo Muani, who joined on loan from Paris Saint-Germain last month, scored twice in three second-half minutes to set Juventus on their way to a 4-1 comeback win at home to lowly Empoli.
That took his tally to three goals in the two matches.
Mattia De Sciglio - who is on loan from Juventus - had got Empoli off to a great start when he headed in a corner in the fourth minute.
Empoli had to play the final six minutes with 10 men after Youssef Maleh was sent off following a second booking.
Dusan Vlahovic netted a highlight solo goal in the final minute and Francisco Conceição added a fourth in stoppage-time to seal the result.
Juventus moved up to fourth. Fiorentina remained a point below the Bianconeri, but having played a match less, after beating Genoa 2-1.
