His 18th goal this season created a 1-1 tie at the 14:51 mark of the first period, and his 19th at 2:18 of the second gave the winners a 2-1 advantage, putting the Capitals on top for good.
It was the first time in seven NHL seasons that Laich scored twice in a game.
Matt Cooke (shorthanded) scored his ninth at 14:41 of the second.
The NHL's leading goal-scorer, Alexander Ovechkin, slapped in his 57th with about 67 seconds left and added an assist.
Goaltender Olaf Kolzig turned away 10 of just 11 shots for the Capitals, who broke a two-game skid and moved closer to securing the eighth and final Eastern Conference playoff spot.
Atlanta's lone goal was scored by Slava Kozlov at 11:41 of the first.
Kari Lehtonen was beaten four times after 37 shots for the Thrashers, who have lost eight straight on the road.