Craig Kimbrel is the best reliever in baseball and the best pitcher on the Atlanta Braves. But Kimbrel didn't pitch in an elimination game because Fredi Gonzalez was only willing to use him for four outs. He also didn't put him in to face Uribe after Puig had led off with a double. Aren't the most important outs those that must happen to strand the tying run in scoring position? Wouldn't that be the best time to use your pitcher who strikes out 1.5 batters per inning? Alas, Gonzalez held Kimbrel to face Schumaker, A.J. Ellis, an injured Ethier and Crawford and Uribe hit a home run to take the lead. No Kimbrel, no game 5.
Gonzalez's lack of imagination with his closer is not unusual. Dusty Baker was fired in part for not using Aroldis Chapman in tied playoff games. In general, baseball managers (and coaches in other sports) manage not to lose rather than to win.
You can't say the same thing about Girardi. In the playoffs and since about the start of August this season, Girardi has played to win. He gave Phil Hughes a very short leash and used his core bullpen members in most critical situations. Obviously Girardi got criticism for using Joba too much, but given that Robertson needed time to rest in September, Logan had pain inhibiting his ability to throw sliders and requiring surgery and Mo was pitching with pain in September, it's hard to argue that he didn't squeeze as much out of them as he could.
In particular with Rivera, Girardi went to him for two innings on several occasions despite having Robertson, one of the better relievers in baseball. It's safer to use Rivera given his long track record, but I think Girardi would have called on Kimbrel last night. If not to start the 8th, then to ensure that Puig was stranded on the base paths.