Please know that a shut-out that is shared between two goaltenders on the same team is credited to neither goaltender. However, the shut-out is credited to the Team.
Furthermore, the goalie in net for the winning goal/save is credited with the win.
Now specific to the St. Louis shutout last night vs. San Jose, Halak was pulled after being injured and Brian Elliott finished the game. Neither goaltender received the shutout, but the STL team did. And the win was awarded to Halak. You can see this at NHL.com.