The full-back’s volley snatched a point for the visitors at the Keepmoat Stadium on Saturday after James Hayter had thought he had given his side the win when he continued his fine goalscoring form with a first-half header.
In a Championship game where chances were few and far between, Hayter needed just one chance to score his fifth goal in as many games.
The striker headed past Swans keeper Dorus De Vries to give the hosts a deserved lead after David Healy had a goal ruled out for being offside.
Healy had several opportunities to put the result beyond doubt for Sean O’Driscoll’s men, but he was foiled by a mixture of poor finishing and fine goalkeeping from De Vries.
He was made to regret those misses when Rangel rifled his volley past Neil Sullivan.
O’Driscoll made just one change from the side that recorded a 3-2 victory at Portsmouth last week as Mark Wilson came in for Shelton Martis.
Brendan Rodgers, meanwhile, made three changes to his Swansea team that triumphed 1-0 over Middlesbrough, with Neil Taylor and Albert Serran replacing the defensive duo of Garry Monk (injured) and Alan Tate (suspended), while Scott Sinclair made way for David Cotterill up front.
The Swans’ makeshift defence looked like they would be in for a tough afternoon when Healy found the back of the net in the fifth minute after he had been put through by Mustapha Dumbuya, however, the Northern Ireland international was flagged offside.
After Darren Pratley had shot wide when one-on-one with Rovers keeper Sullivan, Hayter gave the Yorkshire side the lead after 16 minutes.
The striker met John Oster’s left-wing cross and powered a header past the helpless De Vries to register sixth goal this season.
The visitors have not recouped any points from losing positions this season but they responded well to going behind and James O’Connor nearly put the ball into his own net from Joe Allen’s cross.
Allen also had a deflected strike which went narrowly wide and from the resulting corner, Ashley Williams’ overhead kick missed the target as the Swans started to gain a foothold in the clash.
They went in at the interval still trailing and it was their opponents who appeared to be rejuvenated following the break.
James Coppinger spurned a glorious chance for Rovers when he was clean through on goal as his shot was magnificently saved by De Vries although perhaps Healy was just as guilty when he fluffed his lines on the rebound with the goal at his mercy.
Healy, on-loan from Sunderland, was again at the centre of the action when his looping header from Oster’s cross forced another fine save from De Vries, who tipped the ball over the bar.
The game looked to be petering out, however, in the third minute of added time, Rangel got on the end of a long searching ball and his sensational volley rocketed past Sullivan as Swansea extended their unbeaten run against Doncaster to six games.