Lowest in the Stanley Cup Finals (1971 to present) is actually Tony Esposito, in that wild 8-7 Chicago win over Montreal on May 8, 1973 - seven goals on 30 shots (76.7% save percentage).
The lowest in any series is...Robert Esche, May 2, 2004, in a 7-2 Flyers win over Toronto. Esche played the first period, faced two shots and allowed one goal. Left (officially with an upper body injury) in favor of Sean Burke at the intermission with a 3-1 lead.
Bottom ten:
Robert Esche (5/2/2004) 50%
Steve Baker (4/24/1981) 73.3%
Gerry Cheevers (4/15/1977) 75%
Ron Grahame (4/19/1978) 75%
Mario Lessard (4/7/1982) 75.8%
Martin Brodeur (4/28/2001) 76.2%
Bob Sauve (4/14/1983) 76.5%
Tony Esposito (5/8/1973) 76.7%
Evgeni Nabokov (4/16/2010) 77.3%
Four at 78.3% (Meloche, Gosselin, Fuhr, Moog)