It was a fifth straight win for the Capitals (32-12-6) but the first over Pittsburgh since the Penguins (31-20-1) stopped them 4-3 in the second round of the playoffs last year.
"We just wanted to win this game and it didn't matter how," Ovechkin told reporters. "We have now won five in a row and just want to continue it. It's a big sign for us."
Ovechkin recorded the first and last of four unanswered Washington goals, leveling the scores at 3-3 with a power play conversion at 16:25 in the second.
Ovechkin then watched as his team mates Tomas Fleischmann and Nicklas Backstrom netted goals 53 seconds apart in the third before the dynamic Russian added one final wrist shot with 26 seconds remaining.
Crosby, the face of the NHL along with Ovechkin, recorded his 33rd goal of the season in the first to give the home team a 1-0 lead.
The Capitals now have a three-point lead in the Eastern Conference and have won eight of their last nine.
Goaltender Jose Theodore finished with 35 saves and had 13 in the third where he kept the defending Stanley Cup champions scoreless.
Penguins netminder Brent Johnson filled in for the injured Marc-Andre Fleury and had 28 saves. He performed well before the NHL's top scoring team went on a run beginning late in the second.
The league's two standouts did not disappoint and the supporting cast for each team also performed well. Both Knuble and Fleischmann added assists, while Pittsburgh's Evgeni Malkin and Ruslan Fedotenko both chipped in three assists each.
(Writing by Jahmal Corner in Los Angeles; Edited by Patrick Johnston)