La Divina Assoluta
Well, Bartoli/Henin at Wimbledon 2007 immediately springs to mind. She couldn't have been any more of an underdog and she was being outplayed for a set and a half.
I don't think that's quite what the OP was talking about. A good example from the ATP would be Berdych beating Nadal at the 2015 AO, after previously having lost to him 18 times in a row.Usually its the favorite who breaks down. An underdog who played great was Djokovic when he beat Federer in NY. That forehand down match point was one of the great clutch shots of all time