Frolov's second goal, with 1:16 remaining, gave the Kings an insurance goal. It turned out they needed it because the Ducks' Todd Marchant scored with 38 seconds left.
The Kings ended a seven-game losing streak against the Ducks that included a 4-3 loss Saturday in Los Angeles. The Kings also snapped a five-game overall winning streak by Anaheim, which lost for the third time in regulation this season.
Derek Armstrong broke a 1-1 tie at 9:25 of the second period, picking up the puck during a scramble in front of the Ducks' net and flipping a backhander past Ilya Bryzgalov on the glove side.
After the Ducks opened the scoring on Ryan Getzlaf's power-play goal at 7:00 of the first period, Frolov evened it at 18:11.
Bryzgalov, making his first start since Nov. 17, stopped 30 of 32 shots before he was injured with 12:34 remaining. Jean-Sebastien Giguere replaced him and faced nine shots.
Frolov got his second goal, his 16th of the season, on a short wrist shot in the slot after getting a cross-ice pass from Sean Avery.
Marchant beat Giguere on a rebound, his seventh goal of the season.