Recognizing a change of possession in Washington's end late in overtime, Backstrom headed down ice, received a long pass from T.J. Oshie and beat goalie Carter Hutton for his ninth goal of the season.
Ovechkin tied it at 2 on the power play 8 eight minutes into the third with his 27th goal, and Lars Eller gave the Capitals the lead with 9:11 left. The lead did not last long, with Carl Gunnarson credited with a goal after his shot into pack of players evaded goaltender Braden Holtby with 4:09 remaining.
Holtby made 30 saves for the Capitals. They have won four in a row overall and nine consecutive home games.
Vladimir Tarasenko had a goal and an assist for the Blues. They have lost two in a row and six of their last seven road games.
Alexander Steen snapped a lengthy power-play drought and put St. Louis up 2-1 5:02 into the second period. St. Louis had failed to score on 21 consecutive power plays dating to its Dec. 20 loss at Calgary.
St. Louis dominated the second with had two goals on 12 shots before Washington recorded its first shot on goal in the period.
The Blues tied it at 1 1:18 into the second period on Tarasenko's 18th goal.
