Crosby's goal came 4:09 into the game and gave the Penguins a quick 1-0 lead.
Bill Guerin made the play on the right boards at the red line, feeding Crosby as the Pittsburgh raced through the neutral zone. When Washington's Alexander Semin turned away from the puck at the Caps' blue, Crosby essentially wound up with a 2-on-1, with only defenseman Brian Pothier back.
Crosby raced into the zone, moved from the right to the middle and shot back to the right side from about 20 feet, beating Simeon Varlamov past the glove for his fifth goal of the playoffs.
Pittsburgh shut down Ovechkin for most of the first period, keeping him without a shot on goal until 9:24 remained in the first period. But after Dave Steckel's goal at 13:50 tied the game at 1-1, Ovechkin and his teammates seemed to find their legs.
Ovechkin rifled a power-play shot off the goal post at 15:55, blasted Matt Cooke with a big hit five seconds later and drew a penalty from Cooke for hooking at 16:15, giving Washington a two-man advantage for 59 seconds.
The Caps quickly made Pittsburgh pay when Ovechkin finished off a nice rotation passing play by blasting a shot from the lower left circle behind Marc-Andre Fleury for a 2-1 lead. With Brooks Laich and Semin drawing the defense to the front of the net, Ovechkin had plenty of time and space to rip Semin's erfect pass behind a helpless Fleury for a 2-1 lead at 17:03.
Crosby finished the period with three shots on goal, while Ovechkin had two -- plus two more than were blocked and the one that hit the post.
Neither player scored in the second period, but not for lack of trying.
Ovechkin drilled another post just over two minutes into the period and had a couple of other excellent chances that were stopped by Fleury.
Crosby was wide with a backhander midway through the period after he stole the puck behind the net, and missed another chance by hitting the glass.
But he was also the victim of the best save of the game with 2 minutes left in the period. He raced into the Washington zone with Chris Kunitz, who fed him a perfect pass. Crosby appeared to have a wide-open net for what would have been the go-ahead goal, only to see rookie goaltender Simeon Varlamov get his stick on the shot just as it was ready to cross the goal line.
"I would have liked to put it in," Crosby told NBC's Pierre McGuire after the period. "It's gone; I have to make sure I put the next one in."
Through two periods, each player had a goal. Crosby had five shots on goal, one missed shot, one that was blocked, two hits and was 11-5 on faceoffs in 14:05 of ice time. Ovechkin had taken seven shots on goal, had four blocked, missed three (including the two posts he hit), with two hits, a giveaway, a takeaway and a blocked shot in 15:13.