After Trevor Daley was called for holding Marcus Johansson at 2:40 of overtime, Shattenkirk beat Marc-Andre Fleury with a wrist shot from below the circles for his first goal of the Stanley Cup Playoffs.
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The Penguins lead the best-of-7 series, 2-1. Game 4 is here on Wednesday (7:30 p.m. ET; NBCSN, CBC, TVA Sports).
Pittsburgh played most of the game without center Sidney Crosby.
Crosby left the game 5:24 into the first period after he charged toward the net on a 2-on-1. Alex Ovechkin hit him with his stick, which seemed to make Crosby stumble before Matt Niskanen cross-checked him in the side of his head.
Trainers helped Crosby to the locker room after he was face down along the goal line for a few minutes. Niskanen was given a major penalty and game misconduct for cross-checking.
Penguins coach Mike Sullivan did not update Crosby's condition following the game. He said Crosby and Conor Sheary, who left with an apparent injury after colliding with linemate Patric Hornqvist at 2:24 of the second period, would be evaluated overnight.
Sullivan said the approach would not change if Crosby were unable to play moving forward.
"We're hopeful, first of all, that that won't be the case," Sullivan said. "But I think this group has so much character and talent that we're able to endure the injuries that we have. We've done it all year long. We continued to do it tonight, and we'll continue to do it."