Nicklas Backstrom and Boyd Gordon also scored to help the Capitals pass Tampa Bay in the standings and take the Southeast Division lead.
The Capitals, the division champion the last three years, are in first place for the first time since Dec. 29. Washington has 82 points, one more than Tampa Bay heading into their showdown Monday night at the St. Pete Times Forum.
"We were kind of off and on there tonight," said forward Mike Knuble, who also assisted on Backstrom's goal, "but we did enough to win and at the end got a good result and try to carry it over into tomorrow night."
Goalie Michal Neuvirth made 32 saves, extending his Capitals rookie record with his 22nd victory. The win was Washington's fourth in a row, the team's longest winning streak since Nov. 24-Dec. 1.
"Hopefully this winning streak can give us the confidence we need for the upcoming games," Backstrom said. "We're looking forward now and we have to be focused, especially since we have to play tomorrow in Tampa."
Bill Thomas and David Booth scored for Florida. The Panthers have a season-high five-game losing streak.
"I thought we kind of stayed with them and looked them in the eye and didn't back down," Florida center Marty Reasoner said. "I think we can be proud of that. Obviously, it seems like we're (seeing) too many times where you try to find the positives in losses. With a young group, we're focused on our effort and how we're playing the system. For the most part, we did that and a bounce here or there and both nights we could have come out with wins."
Semin scored on a one-timer from a sharp angle after taking a feed from Marcus Johansson.
Booth tied it for Florida with 2:36 left in the third period on a two-man advantage. He backhanded a rebound from the front of the net.
Gordon gave Washington a 2-1 lead at 10:02 of the second with only his second goal in 44 games this season. With a delayed penalty called on Florida, Gordon got the rebound of John Carlson's slap shot and easily put backhander into an open net.
"It was nice to get one and help the team," Gordon said. "It was a big win for us, and to get these two points heading to Tampa Bay is huge."
Florida outshot Washington 16-6 in the first 20 minutes, but the period ended tied 1-1.
"I thought we deserved to be up a couple after the first period the way we played and instead it's 1-1, so you don't get rewarded for that," Panthers coach Pete DeBoer said. "We stuck with it, though, and we hung around and found a way. I thought we deserved a better fate for how hard we worked."
The Panthers opened the scoring with 4:57 left when Thomas converted a 2-on-1 after getting a feed from Michal Repik. Backstrom tied it with 2:44 to go, one-timing Alexander Ovechkin's pass from the corner.
The assist extended Ovechkin's point streak to four games. The Capitals' last seven victories have been by one goal.
"I think our team plays like we're not going to score too many goals, not just Neuvy," Washington coach Bruce Boudreau said. "So the focus has to be there from the team as a whole. We just have to batten down the hatches and be ready to play those kinds of games every night."
Material from wire services and team media was used in this report.
1 - 0 FLA
1 - 1 Tie
2 - 1 WSH
2 - 2 Tie
3 - 2 WSH