Martin Erat wasted little time in making the adjustments pay off.
The right wing, moved from the fourth line to the second, assisted on three Washington goals and Braden Holtby made 37 saves in the Capitals' 4-1 win.
"He was flying tonight," Ovechkin said of Erat. "He was the best player on the ice for us tonight. He shows who he is."
Joel Ward opened the scoring with a power-play goal for the Capitals, who snapped a two-game skid and finished their five-game homestand 2-3.
Coming off a 2-0 shutout Thursday against the Rangers, Oates dropped Mikhail Grabovski from the second line to the third and Eric Fehr from the third line to a part-time role on the fourth. Laich centered the second line, with Erat moving onto that group.
"You know what, Marty's a good hockey player, has been in this league," Oates said of Erat, a veteran who was acquired last year from Nashville but began the season on the fourth line and was scoreless coming in.
"We lost a couple in a row, we had to make some changes, and he stepped in there and played great for us."
Erat began play with 53 points in 57 regular-season games against Columbus, his highest point total against any team, and continued to punish the Blue Jackets.
Afterward, he preferred to discuss the win rather than his increased ice time and performance.
"It's nice to have a good game, but in the end it's all about the wins, and we got the win and that is the bottom line," he said.
Artem Anisimov spoiled Holtby's shutout at 15:05 of the third.
"You can see how we play when he is on fire," Ovechkin said of Holtby. "We have a lot of confidence, especially when he makes a big save and we can see he feels the puck."
Sergei Bobrovsky had 35 saves for the Blue Jackets, who have lost four straight.
"We unraveled," Columbus coach Todd Richards said. "I think even after those first two goals, we started to go after them, but we weren't good enough. We got what we deserved. I think the chances were there."
Washington went up 1-0 early in the second period thanks to its top-ranked power play.
Columbus peppered Holtby for several minutes to no avail.
Then Washington's Steve Olesky came down the right side and made a nice delaying move to get his shot off. Bobrovsky made the stop, but Laich shoveled the rebound home to make it 2-0 at the 7:43.
Washington added some insurance in the third when Erat stole a pass in the Columbus zone and fed Brouwer in front. Bobrovsky made a point-blank save, but Brouwer got the rebound, moved to his right and put the puck past the fallen goaltender at 4:20.
"They got that third (goal) and it just cracked us, I guess," Blue Jackets RJ Umberger said. "We turned the puck over. They capitalized on their chances tonight and we didn't."
Just over two minutes later, with Washington on a power play, Ovechkin beat Bobrovsky with a one-timer from his familiar spot in the left circle for his seventh goal of the season.
"As far as the third period, we're letting each other down as far as our play in front of our goalie," Richards said. "Disappointing the way the game ended."
The Capitals controlled play for much of a scoreless first period, when Bobrovsky made 14 saves.
Columbus had an excellent chance when Ryan Johansen picked up a loose puck in the Washington zone midway through the period. He skated in alone on Holtby, but his shot hit the right post.
The Blue Jackets recalled F Jack Skille from the AHL's Springfield Falcons and assigned F Sean Collins to their AHL affiliate. ... Washington D John Erskine missed his fourth game (upper body injury) and C Jay Beagle was a healthy scratch. ... LW Nick Foligno, C Ryan Craig, and D Dalton Prout were the Columbus scratches. ... It was the teams' first meeting since Dec. 31, 2011. They'll play each other three more times this season as members of the Metropolitan Division.