"If we have a chance to go and score goals we will, but sometimes one mistake can cost a lot," Ovechkin said. "We've talked about it here in the locker room and the most important thing is when you get that lead, you try to protect that lead."
Braden Holtby made 24 saves for his fifth straight victory. Eight of the Capitals' wins during their streak have been decided by one goal.
"We like being in tight games this year and we find a way to get a goal at the right time," said Brooks Laich, who scored his 16th goal in the first period.
Washington played without deadline acquisition Jason Arnott, who is expected to miss at least the next two games with an undisclosed injury.
Tuesday's victory opened a season-high six-game road trip, which isn't necessarily a bad thing for the Capitals. They've won six straight away from home as they prepare to face the Red Wings, who haven't fared well recently at Joe Louis Arena.
Detroit (41-20-8) won 5-3 at St. Louis on Saturday, one day after ending a three-game home skid with a 2-1 overtime victory against Edmonton. The Red Wings are 18-11-4 at home on the season, but 8-10-2 there since the start of December.
Pavel Datsyuk had an assist and the game-winning goal against the Blues, giving him 10 goals and seven assists in 17 games since returning from a broken wrist.
Jimmy Howard made 26 saves and earned his 33rd victory of the season despite allowing St. Louis to tie the game with two goals early in the third period.
"We didn't get frustrated, we just settled down," Howard said. "I thought we played another great game minus the first five minutes of the third period."
Niklas Kronwall had a goal and two assists for his first three-point game since Nov. 11, 2009.
During their three days off, the Red Wings saw their lead over San Jose for second place in the West dwindle to two points, although Detroit has two games in hand.
Washington and Detroit split two games in 2009-10, with each winning on home ice. The Capitals last beat the Red Wings at Joe Louis Arena on Nov. 24, 2003, a 4-1 victory. They've lost twice there since.
AccuScore has powered more than 10,000 simulations for every NHL game on ESPN.com, calculating how each team's performance changes in response to game conditions and opponent's abilities. Each game is simulated and the game is replayed a minimum of 10,000 times to generate forecasted winning percentages.