Semin gave Washington a 3-2 lead when he wristed a shot past Al Montoya. Semin now has 22 goals, two behind Alex Ovechkin — who assisted on the tally — for the team lead.
Brooks Laich and Mike Knuble also scored for the Capitals, who trailed 2-1 entering the third period after losing 6-0 at home to the New York Rangers on Friday night.
Washington is 10-0-3 in its past 13 meetings with the Islanders, including six straight wins on Long Island.
Kyle Okposo and Travis Hamonic scored and Montoya made 19 saves for the Islanders, who lost their third straight despite leading 2-0.
The Islanders took the first 11 shots of the game without scoring, but grabbed a 1-0 lead with their next shot.
Okposo skated in on a 2-on-1 break, moved from the wing to the slot, and fired a wrist shot that beat Neuvirth high at 13:48.
The Islanders jumped ahead 2-0 just 33 seconds into the middle period when Hamonic took a slap shot from the right point that eluded traffic and Neuvirth.
Laich cut the Capitals' deficit in half at 9:44 when he sent a wrist shot from the left side between Montoya's pads.
Knuble tied it at 2:24 of the third period when he backhanded a rebound past Montoya.
Notes: Among Washington's scratches were Marco Sturm, claimed Saturday off waivers from the Los Angeles Kings, and goalie Seymon Varlamov. Todd Ford served as Neuvirth's backup. ... The Islanders placed C Rob Schremp and G Nathan Lawson on waivers. ... This was the first half of a home-and-home series that will conclude Tuesday in Washington. ... The attendance was 16,250, the Islanders' biggest home crowd of the season.