Crosby has scored 13 points (three goals, 10 assists) during his streak.
Jeff Carter scored his third goal in two games for the Penguins (13-8-5), who have won three straight. Tristan Jarry made 29 saves for Pittsburgh, which led 3-0 entering the third period.
"I thought we were quick to pucks in the offensive zone, and for me that's when our team is at its best, when we're up in fives and we're playing an in-your-face style of play," Pittsburgh coach Mike Sullivan said. "We weathered the storm, but I thought the first 40 minutes in particular we were real good."
Evgeny Kuznetsov and Lars Eller scored for the Capitals (16-5-6), who lost in regulation at home for the second time (9-2-4). Ilya Samsonov made 29 saves.
"I thought mentally we were just a step behind," Washington forward T.J. Oshie said. "We shot ourselves in the foot quite a bit. We did get some chances, we got some breaks and weren't able to put it in the back of the net, and sometimes we wouldn't get a shot off. Just not our best game."