Justin Williams added an empty-netter with 1:41 left.
The Kings finished 3-2 on their trip, and have won four straight in Texas while outscoring the Stars 16-5.
Brad Richards struck on the power play and Brandon Segal also scored for Dallas. The Stars have scored only four goals in their last three games.
Kari Lehtonen stopped 11 of 15 shots before being sent to the bench in the third period as the Stars lost for the fourth time in five games, including the first three of a season-high six-game homestand.
Ponikarovsky broke a 1-all tie off a rebounds at 13:05 of the second period, and Simmonds made it 3-1 at 13:14.
Simmonds, who assisted on Ponikarovsky's goal, went in on a breakaway, crashing into Lehtonen as he scored and knocking the net off its moorings. The Stars claimed the goal shouldn't have counted.
But after a video review, the goal stood because the puck entered the net before it was dislodged.
When Mitchell scored short-handed at 4:40 of the third period to make it 4-1, Stars coach Marc Crawford hooked Lehtonen and brought in Andrew Raycroft for his first action of the season.
Segal's even-strength goal at 10:10 of the third period pulled Dallas to 4-2.
The Kings capitalized 11 seconds into a 5-on-3 advantage on Brown's close-range goal at 3:30 of the opening period.
The Stars took advantage of a 5 on 3 of their own at 16:03 of the first period when Richards' shot from the left point got past a screened Quick to tie it at 1.
NOTES: Stars rookie D Philip Larsen made his season debut and got his second career assist. Larsen was brought up from Texas of the AHL to fill in for Stephane Robidas, serving an automatic one-game league suspension after drawing his second boarding major in 41 games Tuesday night in a loss to Anaheim. Larsen, who played two games for Dallas last season, was on the top defensive pairing with Nicklas Grossman. ... Kings D Drew Doughty remains out while he recovers from a concussion, with no timetable for his return.
|PPG - Dustin Brown (5) ASST: Jack Johnson (5), Anze Kopitar (6)|
1 - 0 LAK
|PPG - Brad Richards (3) ASST: James Neal (5), Loui Eriksson (3)|
1 - 1 Tie
|Alexei Ponikarovsky (2) ASST: Wayne Simmonds (3), Jack Johnson (6)|
2 - 1 LAK
|Wayne Simmonds (3) ASST: Jack Johnson (7), Rob Scuderi (1)|
3 - 1 LAK
|SHG - Willie Mitchell (1) ASST: Jarret Stoll (4)|
4 - 1 LAK
|Brandon Segal (1) ASST: Brian Sutherby (1), Philip Larsen (1)|
4 - 2 LAK
|EN - Justin Williams (4) ASST: Davis Drewiske (3), Willie Mitchell (4)|
5 - 2 LAK
|Jamie Benn Holding the stick against Brad Richardson|
|Karlis Skrastins Slashing against Anze Kopitar|
|Matt Greene Interference against Jamie Benn|
|Justin Williams Hooking against Loui Eriksson|
|Jarret Stoll Boarding against Philip Larsen|
|Steve Ott Hooking against Alexei Ponikarovsky|
|Matt Greene Cross checking against Mike Ribeiro|
|Brian Sutherby Fighting (maj) against Kyle Clifford|
|Kyle Clifford Fighting (maj) against Brian Sutherby|
|Nicklas Grossmann Boarding against Brayden Schenn|
|Kevin Westgarth Roughing against Nicklas Grossmann|
|Dustin Brown Slashing against Mark Fistric|
|Rob Scuderi Hooking against Mike Ribeiro|