Trailing 1-0 for most of the game, the Capitals erupted in the late going to notch their third win over the Senators this year.
Washington tied it 7:15 into the final frame when Ottawa defenseman Chris Phillips tried to hit Daniel Alfredsson with a pass in the Sens' zone, but it jumped Alfredsson's stick and went to straight to Laich, who blasted a one-timer past Brian Elliott to tie the score.
Only 45 seconds later, Carlson let a slap shot fly from the left point directly off a face-off win and got it past a screened Elliott to put Washington in front 2-1.
Jason Chimera added an insurance tally and Michal Neuvirth made 22 saves as the Caps broke a three-game losing streak.
Mike Fisher scored and Elliott turned aside 23 shots in Ottawa's loss.