Ovechkin made it 3-1 at 15:12 of the second with his first goal in five games after Strome picked Tarasenko off along the right boards and fed Ovechkin alone in the slot.
Carlson cut it to 3-2 at 17:36 with a short-handed goal in his 900th NHL game, finishing a 2-on-1 after Schenn missed a shot high.
O'Reilly made it 4-2 on a backhand at 18:02 following a high-low pass from Josh Leivo.
The Capitals outshot the Blues 22-3 in the third and 18-9 in the second.
"We just sat back, turned pucks over," Schenn said. "Didn't close out plays defensively and forced us to play a lot of time in our own end.
"That's what happens. You give up 50 shots, you're just probably not [playing] hard enough defensively, and guys that are over there, they have a ton of skill. They're going to make the most of it. And we relied on our goalie way too much."
NOTES: Ovechkin tied Bryan Trottier for 18th all-time in NHL career points (1,425). He has 34 points (19 goals, 15 assists) in 23 games against St. Louis. ... Strome had two assists to give him nine points (one goal, eight assists) in nine games against the Blues. ... Carlson has three goals and two assists in the past four games. ... St. Louis is 5-0-1 in its past six games against Washington. ... Tarasenko has 12 points (eight goals, four assists) in 12 games against the Capitals. ... O'Reilly has six points (three goals, three assists) in his point streak.