Trailing 4-2, the Kings scored twice in the final 3:18 of regulation. Dallas got three minor penalties in a 63-second span, giving Los Angeles a two-man advantage for 1 minute, 10 seconds late in regulation. Handzus scored his second of the game during the 5-on-3 power play.
Anze Kopitar tied it with 14 seconds left, playing the puck off a broken stick left behind by teammate Dustin Brown and backhanding the puck toward the net. It caromed off the skate of Dallas defenseman Stephane Robidas and past Marty Turco for Kopitar's 22nd goal of the season.
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The Kings, who outshot Dallas 21-3 in the third period, ended a four-game losing streak when Handzus played Jack Johnson's wide slap shot off the end boards and circled the net before putting a wraparound just inside the left post for his 13th goal.
Erik Ersberg started for only the third time in Los Angeles' last 20 games, stopping 15 of 19 shots one day after signing a two-year contract extension. Jonathan Quick took over for Ersberg at the start of the third period with Los Angeles trailing 4-2.
Kopitar also has two assists, Alexander Frolov had a goal and an assist and Drew Doughty added two assists. It was the first time the Kings won after trailing by three goals since Nov. 10, 2007, when they overcame a 4-0 deficit in the third period and won 6-5 in OT.
Mike Ribeiro, Loui Eriksson and Steve Ott each had a goal and an assist for Dallas and rookie James Neal scored his 21st goal. Turco made 35 saves -- 19 in the third period -- as the Stars lost for the sixth time in seven games after a 10-3 stretch.
Dallas right wing Jere Lehtinen did not play because of an undisclosed upper body injury after getting hit by San Jose's Rob Blake in Wednesday's 4-1 victory. The three-time Selke Award Winner as the league's top defensive forward returned to Dallas to get checked by a doctor, and will also miss Friday night's game at Anaheim.
The Stars appeared to be well in control with a 3-0 lead when the game suddenly turned on a penalty against newly acquired Steve Begin for cross-checking Oscar Moller with 4:36 remaining in the second period. Handzus got Los Angeles on the board just 17 seconds later, tipping in Kyle Quincey's one-timer from the right point.
The Kings kept the pressure on Turco, who left a bad rebound on Dustin Brown's wrist shot from the right circle and was left defenseless as Frolov easily converted the rebound into a wide-open net for his 27th goal at with 3:46 left in the period.
Dallas coach Dave Tippett used a timeout to settle his club, and Ott restored the Stars' two-goal margin by poking his 13th goal past Ersberg during a goalmouth scramble just 14 seconds before the second intermission.
The Stars, struggling to get back into a playoff spot with Brenden Morrow, Sergei Zubov, Brad Richards and Toby Petersen all on injured reserve, opened the scoring at 5:49 of the second period. Eriksson recorded his team-high 29th goal, beating a sprawling Ersberg to the glove side after Mike Modano set him up in the low slot.
Modano's assist increased his career total to 781, tying Brian Leetch for second place among American-born players behind Phil Housley's 894. Modano holds the records for goals (543) and total points (1,324) by an American-born player.
Notes:@ Lehtinen missed the first 14 games of the season with an upper body injury, then returned for three games before sitting out the next 14 due to a groin injury. Dallas is 12-13-4 in his absence. ... C Brendan Morrison played his first game with Dallas after being claimed off waivers from Anaheim on Wednesday. ... D Sean O'Donnell's fighting major in the second period gave him 860 penalty minutes in a Kings uniform, surpassing current assistant coach Mark Hardy for fourth place on the franchise list behind Marty McSorley, Jay Wells and Rob Blake. ... Dallas' penalty-killing unit had allowed only five goals in its previous 48 short-handed situations coming in. ... Turco had made 35 consecutive starts before sitting out the win over the Sharks. ... Quincey leads Los Angeles with 25 points on the power play, including 23 assists.