Hill stopped 39 of 42 shots in Thursday's 3-2 overtime loss to the Stars in Game 4.
Hill's five-game winning streak came to an end as Joe Pavelski scored in the extra session to keep the Stars alive. Prior to Thursday, Hill had given up three or more goals in just three of his eight playoff appearances. The 27-year-old is at 6-2 with a 2.07 GAA and a .938 save percentage through nine games. He'll likely start again on home ice in Game 5 on Saturday.