The Serbia striker headed in Georginio Wijnaldum's cross with seven minutes to go of boss Rafael Benitez's home debut.
Jermain Defoe had volleyed the visitors ahead just before the break.
The draw leaves both in the bottom three, with 18th-placed Sunderland a point and a place ahead of Newcastle but two points from safety.
It is a result that ends a four-game losing streak for Newcastle, during which Steve McClaren was sacked as manager and replaced by former Liverpool and Chelsea boss Benitez.
Sunderland have drawn their last three matches.
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While not the victory they so badly needed, the draw does mean Newcastle have ended a six-match losing streak against their fierce rivals, dating back to April 2013.
This was the least they needed after Norwich's victory at West Brom on Saturday had opened some daylight between the 17th-placed Canaries and the bottom three.
And despite the huge challenge still ahead, the manner in which they clawed their way to a point will give Benitez some hope that he can fashion an escape act over the next two months.
For much of the game a somewhat ragged and ill-disciplined Newcastle were second-best to a Sunderland side who have been instilled with a renewed efficiency and spirit by manager Sam Allardyce.
After falling behind, the home side offered plenty of effort but precious little quality in the second half, with an Ayoze Perez volley at the back post, which was cleared off the line by Yann M'Vila, the closest they came to a goal.
But Mitrovic's late intervention - the sixth he has scored since joining the club last summer for £15m - gives them confidence before six April fixtures that will go a long way to deciding their fate.
Next up; Norwich at Carrow Road on 2 April.
Sunderland were seven minutes from moving out of the relegation zone so to find themselves in the bottom three heading into the international break is an undoubted blow.
This is a game they should have won. They played more as a unit throughout and fashioned the better chances.
Defoe's goal - coming after Rob Elliot had saved a shot from Fabio Borini and Chancel Mbemba had failed to properly head clear - was his eighth in his past 11 appearances, but he could have scored more.
Before his opener he fired over from inside the box and poked a first-time shot from Borini's cross inches past the near post.
And had Elliott not produced a wonderful one-handed save to deny Patrick van Aanholt's angled 12-yard drive, it would have been 2-0 just before the hour mark.
Ultimately, though, it was their defensive frailty that cost them as a DeAndre Yedlin foul throw set up the move from which Mitrovic scored the 39th goal the Black Cats have conceded away from home this campaign and extended their run of games without a clean sheet to 17.
Newcastle boss Rafa Benitez: "The positive thing for me is we have eight games to play and the reaction today from the players was positive.
"To win would have been perfect but when you are losing in the first half and keep the same gap, it's positive.
"The main thing was that the fans supported us today and we want that in every single game.
"I think we can stay up. We have to keep working, I believe they can play better and from what I have seen today in the second half, they can do well."
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Sunderland boss Sam Allardyce: "For me, if we don't start getting these clean sheets it's going to be a massive problem. We are a team that has to score twice to win.
"Sadly we didn't get the second goal and we conceded late on again. We had the chances to put the game to bed, but missed them.
"Second half, I don't know why we sat in and let Newcastle come at us. Maybe that was the size of the game, but in the end we haven't done that and it's two points dropped.
"We should have won this one. We need four wins from the last eight, so it's now must-win rather than draw."
Newcastle travel to Norwich on 2 April (15:00 BST) before visiting Southampton a week later.
Sunderland are home to West Brom on 2 April (15:00 BST) and leaders Leicester on 10 April (13:30 BST) before travelling to Norwich themselves on 16 April (12:45 BST).
Aleksandar Mitrovic rescued a point for Newcastle against relegation rivals Sunderland as a fiercely contested Tyne-Wear derby ended in a draw.