According to hockey-reference.com, since the 1987-88 season (the first year where they have game-by-game logs), there have been 43 goalies who won a game while making 5 or fewer saves. There were three more who did so in the playoffs.
On three occasions, a goalie won a game without making any saves. Twice it was Craig Billington - how's that for a trivia question!
1. Craig Billington - December 31st, 1996 - played 12 seconds and faced no shots. He was in relief of Patrick Roy (who stopped 21 of 22 shots). Chicago's Chris Chelios took a penalty at 10:06 of the second period, giving Colorado a powerplay. Chicago's James Smith took a penalty at 11:23, giving Colorado a shortened two-man advantage. The Avalanche replaced Roy and put Billington in net (presumably to give their top powerplay unit a breather). Twelve seconds later, Sandis Ozolinsh scored on the powerplay (11:35). This was Colorado`s second goal in a 4-1 win, so Billington "won" the game thanks to his invaluable 12 seconds of contribution.
2. Craig Billington - December 31st, 1998 - this time he played 1:52, again in relief of Roy, who stopped 27 of 29 shots in a 4-2 victory. Similar circumstances. Anaheim`s Johan Davidsson took a penalty at 15:54 of the second period, giving Colorado a powerplay, then Kevin Haller took a penalty at 17:18, giving Colorado an abbreviated two-man advantage. Billington replaced Roy (again, presumably to give Sakic and others a rest). Hejduk scores the team`s third goal (in a 4-2 win) 1:52 later. (Note that the Hockey Summary Project says that Billington played 2:18, but I think the time on Hockey-Reference is more reasonable since it perfectly coincides with a logical analysis of game events. Regardless, it also gives him credit for stopping zero shots).
3. Richard Bachman - March 29th, 2013 - played 2:32 in relief of Kari Lehtonen (who stopped 30 of 33 shots in a 5-3 win). This is a fairly recent game, but I don`t remember it. The circumstances appear to be similar - two Minnesota players (Ryan Syter and Mikko Koivu) both took penalties at 2:00 of the third period, giving Dallas a two-man advantage. Just ten seconds later, Jamie Benn scores (giving the Stars their 4th goal in a 5-3 win). Bachman was obviously in net when this happened. Since he played 2:32, my guess is he was put in net at 2:00 (start of the two-man advantage) and was kept on the ice after the Stars scored at 2:10. He was then replaced by Lehtonon at 4:32 (2:32 after he entered the game) when the Stars` Aaron Rome took a penalty thus creating a stoppage in play.
Ray Emery is the only goalie (dating back to 1988) with more than three "wins" in a game where he made five or fewer saves (on all four occasions playing less than half the game, and making 15 saves and 17 shots across those four wins)! That`s four of his (currently) 145 career victories.
For all the criticism that Martin Brodeur gets, he was only on the list once (playing 26:38 and stopping all five shots against Atlanta). When the Leafs were infamously shut down by the Devils in the playoffs (game 6 in 2000 second round), he faced six shots (and stopped all of them), so he doesn`t appear on this list for that match.
