Fiala tied it 1-1 at 5:21 of the second period off a rebound of a Carl Grundstrom shot that deflected off Wedgewood's glove.
The Stars then scored three goals in 1:30 to open a 4-1 lead.
Robertson made it 2-1 on the power play at 9:01 on a one-timer from the top of the right circle.
"We were working," Heiskanen said about the power play. "I think we have two really good units, and we need to be there, top-five [in the NHL] at least."
Tyler Seguin pushed it to 3-1 at 10:17 from just inside the right circle, and Hintz scored 14 seconds later on a breakaway at 10:31.
Kaliyev's power-play goal cut it to 4-2 at 14:37. Viktor Arvidsson sent a no-look, between-the-legs pass through the crease that deflected off Stars defenseman Esa Lindell's stick to Kaliyev for a tap-in.
"We know how good we can play and how good we can be as a team," Kings forward Phillip Danault said. "We want to improve every game, and on a back to back, it's a great opportunity to steal points. Obviously, a disappointing ending tonight."
Joe Pavelski scored on the power play at 18:37 for the 5-2 final.
"There's no need for the frustration level to be high right now," Los Angeles forward Anze Kopitar said. "We played a good game last night. We didn't get it done tonight. There's another game on Thursday [and] 2-1 on the trip would be a pretty good trip, so we're going to rest tomorrow and get back at it on Thursday."
NOTES: Heiskanen had four shots in 19:15 after missing three games with an upper-body injury. His two assists gave him 101 in the NHL. … Stars defenseman Ryan Suter played his 1,290th NHL game to pass Mathieu Schneider for third among United States-born defensemen behind Chris Chelios (1,651) and Phil Housley (1,495). … Fiala extended his point streak to five games (two goals, six assists). … Kings forward Gabriel Vilardi had his four-game goal streak end.