Andrei Vasilevskiy made 20 saves for the Lightning (17-15-3). Kristers Gudlevskis made three saves in relief.
Carlson scored 55 seconds into the first period for a 1-0 lead. His slap shot from the blue line deflected off two Lightning defensemen and over Vasilevskiy. The goal was Carlson's first at even-strength and second of the season.
Carlson's second goal of the game came at 15:42 and gave the Capitals a 2-0 lead.
"They got the 2-0 lead and the irony of the whole thing is we only gave them four shots in the last 15 minutes of the first period," Lightning coach Jon Cooper said. "So, as ugly as it looked, they did all their damage in the first five minutes and that kind of changed the game. The kicker, though, was when we didn't score in the first five minutes of the second. We were all over them. We needed the next goal and, ultimately, they weathered that storm and got the third one and that was it."
Ovechkin scored his 15th goal of the season at 10:48 of the second period for a 3-0 lead. Defenseman Dmitry Orlov chipped the puck ahead to Ovechkin, who scored on a breakaway.
Johansson scored at 8:33 of the third period to make it 4-0. Backstrom sent a cross-ice pass to Johansson as he left the penalty box, and Johansson scored his 13th goal of the season on a breakaway.