Substitute Rooney curled in from the left-hand corner of the penalty box for his 250th United goal, one more than Sir Bobby Charlton.
Stoke looked set for a third straight Premier League win, clinging to a lead given to them when Juan Mata poked Erik Pieters’ cross into his own net.
United wasted chances, hit the woodwork and were denied by Potters keeper Lee Grant.
But their 25th and final effort at goal preserved a 17-game unbeaten run, albeit if the dropped points mean they lose ground in the race for the top four.
They are three points behind fourth-placed Arsenal and 11 off leaders Chelsea, who both play on Sunday.
Rooney, so often the fulcrum of the United side since joining from Everton as an 18-year-old in 2004, has had to make do with a bit-part role under Jose Mourinho this season.
Indeed, this 546th appearance came from the bench, but still delivered a moment of history.
United had been frustrated for so long by Stoke’s stoic defence and their own wastefulness, and a free-kick awarded just outside the home penalty area looked to be the visitors’ last chance as five minutes of added time ticked down.
Rooney, largely ineffective since joining the action, looked prime to cross, but instead arced a wonderful, dipping, right-footed shot inside the far post past the previously unbeatable Grant.
Not only did the 31-year-old pass the mark of Charlton that had stood since 1973, but he gave United a point that looked to have gone.
Rooney’s intervention was all the more dramatic given the struggles of his team-mates on a bitter afternoon in the Potteries.
United had almost all of the play – 65% of the possession, 25 efforts on goal to Stoke’s six, almost a third of the game was played in City’s defensive third – and yet the visitors could barely find a way through.
Soon after deflecting into his own net, Mata dinked over from close range with the goal at his mercy, while Grant made excellent saves from Marouane Fellaini and Paul Pogba.
Zlatan Ibrahimovic was strangely subdued and on more than one occasion he opted to pass when an effort on goal looked the better option.
An isolated figure in the first half, the former Sweden forward gained more support in the second – Marcus Rashford providing pace and incision down the left, fellow substitute Jesse Lingard hitting the top of the crossbar.
It all looked to count for nothing until Rooney’s late moment of magic gave the visitors a point they totally deserved.
