Milano made it 2-0 when he exited the penalty box, controlled a Carlson pass and beat Vasilevskiy on a breakaway at 7:03 of the second period for his first goal with Washington.
"It was just kind of reactionary," Carlson said. "It worked out well, the puck jumped over my stick and I turned that way and gave it a little extra juice just in case to get it out of the zone, first off because I was tired, but it worked out perfect. He made an awesome move and there we go."
Milano had served a five-minute match penalty for Nicolas Aube-Kubel, who was ejected for an illegal check to the head of Lightning defenseman Cal Foote, who left the game.
"Not great," Tampa Bay coach Jon Cooper said when asked about Foote. "He obviously couldn't come back. That's a tough hit. That defines the word blindside. It's too bad we're playing them again [Sunday] because I doubt [Foote] will be around to see the game."
Aliaksei Protas increased the lead to 3-0 when he knocked in the rebound of Nick Jensen's shot at 14:25.
Conor Sheary received a pass from Mantha and beat Vasilevskiy from the slot on the rush to make it 4-0 at 4:53 of the third period.
Perbix cut it to 4-1 when he scored on a one-timer from the top of the left circle at 12:09.
"We want to get back on track, obviously," Lightning defenseman Victor Hedman said. "You can't get frustrated, that's the bottom line. We believe in ourselves, but it'll be good to get these guys once again."
Milano, who signed with the Capitals on Oct. 16, made it 5-1 when his pass attempt to Evgeny Kuznetsov deflected in off Stamkos at 17:45.
"It has been pretty smooth," Milano said of joining Washington. "Everyone has been taking care of me, and obviously a great group of leaders and older guys that I definitely am looking up to."
NOTES: Tampa Bay defensemen Erik Cernak and Mikhail Sergachev each left the game late in the third after blocking an Alex Ovechkin shot. Cooper did not have an update. … Lightning forward Nikita Kucherov had his 11-game point streak end (six goals, 14 assists). He was held without a point for the second time this season (Oct. 14 at the Columbus Blue Jackets). … Tampa Bay forward Brayden Point had his five-game point streak end (two goals, seven assists). … Carlson moved past Michal Pivonka for the fifth-most points in Capitals history; he has 134 goals and 466 assists in 897 games in 14 seasons, all with Washington.