Brian Willsie scored for the Kings, who have won four of five since opening the season 1-5. The win was their first over Dallas since April 1, 2006, a 1-0 victory at Staples Center.
Jere Lehtinen scored for Dallas and Marty Turco made 28 saves, 18 in the second period. Turco moved into third place on the franchise's all-time list for games played by a goaltender behind Cesare Maniago (420) and Giles Meloche (328).
The Kings, coming off victories over Vancouver and Nashville, have won three straight for the first time since a five-game streak Feb. 11-March 7, 2006. Last season marked the first since 1985-86 in which Los Angeles failed to win more than two straight.
Frolov put Los Angeles ahead to stay with 18:20 remaining, getting a step in front of Mike Modano in the slot and beating Turco to the stick side after Derek Armstrong set him up with a no-look, backhanded centring pass from behind the net. Frolov has scored in three straight games following a season-opening eight-game drought.
Brenden Morrow, playing in his 500th NHL game, set up the first goal at 16:05 of the first period. His pass from behind the net went between the legs of Kings centre Patrick O'Sullivan and onto the stick of Lehtinen, whose 10-foot wrist shot beat LaBarbera high to the stick side.
The Kings tied it exactly halfway through the second period. Kyle Calder dug the puck out of a crowd in the right corner, circled the net and gave it to Michael Cammalleri, whose short wrist shot was turned aside by Turco before Willsie converted the rebound.
Notes: Dallas' 8-0 mark against the Kings in 2006-07 was just the ninth season sweep of eight or more games in NHL history. The Stars won the first meeting this season, 5-1 at Dallas. ... The Kings, in conjunction with the Salvation Army, will begin collecting donations at their next four home games to aid those left homeless by the Southern California wildfires. During the Nov. 10 games against Dallas, each player will wear a commemorative Southern California Fire Department patch on his jersey, and the jerseys will be auctioned with all proceeds going to the fire victims. ... LaBarbera has stopped 89 of the last 92 shots he has faced. ... Dallas defencemen have accounted for one goal through the first nine games. Last season they scored 43 goals, including a career-high 19 by Philippe Boucher.