Jose Mourinho's side took the lead when Oscar whipped a free kick which was intended as a cross beyond Lukasz Fabianski.
The visitors were soon level through Andre Ayew, who equalised from close range, but the Blues went back in front seconds later as Willian's cross deflected in off Federico Fernandez.
But Swansea equalised again after the interval when Bafetimbi Gomis converted a penalty, having been brought down by the onrushing Courtois, who was shown a red card by referee Michael Oliver.
