Frolov, who has scored four goals in four games, was left alone in front of goalie Roberto Luongo and fired the rebound of a Kevin Dallman shot past Luongo at 1:48 of overtime. Luongo, who had no chance on the play, finished with 40 saves.
Patrick O'Sullivan also scored for Los Angeles, who earned coach Marc Crawford the win in his return to Vancouver. Crawford registered a club-record 246 wins with the Canucks before being fired after last season.
Sami Salo and Trevor Linden scored for Vancouver (27-19-3).
The Kings (17-28-6) earned their first overtime win of the season in seven tries but remained last in the Western Conference.
Vancouver, with 10 victories in the last 12 games, could've moved atop the Northwest Division with a win but remains tied for first with the Calgary Flames, one point ahead of the Minnesota Wild.
Vancouver was outshot 22-16 in the second period but Linden got the only goal to pull his team into a 2-2 tie heading into the third.
Standing in front of Kings goalie Sean Burke, Linden deflected Kevin Bieksa's pass from the corner past Burke, a 17-year NHL veteran who turns 40 on Monday.
Luongo kept his club in the game in the second with several key saves, including close-in chances by Rob Blake and Craig Conroy.
The Kings had five shots on Luongo and a 2-0 lead by 12:26 of the first.
O'Sullivan, called up Thursday from the AHL's Manchester Monarchs, scored on his first shift when Bieksa fell with the puck in the corner.
Flashy rookie Anze Kopitar dug it out and passed to an uncovered O'Sullivan, who scored his second goal in 13 NHL games this season.
Frolov was also left alone long enough to backhand in his own rebound for his team-leading 24th goal and third in four games.
Salo split the margin with a shot that somehow beat Burke, the Kings' fifth goalie this season.
The puck hit Brent Sopel's stick and bounced off Mattias Norstrom's shoulder before falling behind Burke, who was claimed off waivers from Tampa Bay.
NOTES: Fans gave Crawford a smattering of applause when he was shown briefly on the scoreboard screen during the U.S. anthem . . .The contest was the first of a four-game homestand for Vancouver while the Kings play seven of their next eight on the road . . . A sore groin kept Willie Mitchell off the Vancouver blue-line. Yannick Tremblay was recalled from AHL Manitoba to replace him . . . Canuck centre Tommi Santala is practising again after being sidelined by a knee injury since early December.