DALLAS -- The Stars have their first win of 2014.
"We're pretty happy with that one," Garbutt said. "We got some tough breaks in the little slide here, and I think tonight we got some breaks and bounces."
Jamie Benn scored a rare power-play goal for the Stars, who had not won since New Year's Eve. They entered 29th in the NHL with the man advantage.
Benn also assisted on the first goal of the game by Erik Cole, only 14 seconds in. Cody Eakin and Trevor Daley each had a goal and an assist for Dallas, which built a 4-1 lead 1:10 into the second period.
"Not a good way to start the game," Edmonton coach Dallas Eakins said. "Going through the game in my end, it seemed like we made three mistakes and they ended up in our net and you can't recover."
The final Stars goal came on Daley's shot into an empty net in the last minute.
Justin Schultz and Sam Gagner scored for Edmonton, with Taylor Hall assisting on both goals.
After the opening faceoff, Daley skated in from the left side, drawing goalie Ilya Bryzgalov's attention. Daley then passed across to Cole, who swept the puck into the open right side.
Edmonton tied it at 3:20 when Hall passed to Schultz in the lower right circle. He skated across the front of the net and flipped the puck over Dallas goalie Kari Lehtonen, who finished with 31 saves.
Garbutt's third goal in two home games against Edmonton gave the Stars a 2-1 lead at 8:35 of the first.
"To get that goal right away was important," Stars coach Lindy Ruff said. "Obviously, if you sit right there at 1-1, a lot of things can happen."
A pregame talk between Ruff and Garbutt seemed to help.
"I had a conversation with him again about some plays in the previous game that I didn't like," Ruff said.
"I thought Ryan's play was excellent. Tonight might have been one of his best."
Benn's power-play goal followed less than 2 minutes later.
Tyler Seguin passed from the top of the right circle to Benn on the left. His drive beat Bryzgalov.
It was only the seventh goal at home with a man advantage in 81 opportunities for Dallas this season. Overall, the Stars entered with a 12.4 percent success rate (20 for 161).
"Tyler made a great play and [Benn] a great shot. We've had that same look a few times and haven't scored," Ruff said. "Hopefully, that leads to better times ahead for the power play."
Dallas' fourth goal came at 1:10 of the second by Eakin. Antoine Roussel sent a centering pass to Eakin from the right corner.
The Oilers controlled play for most of the second period but came away only with Gagner's goal. He got the puck in the crease after Lehtonen got tangled up with Daley.
Benn's goal was his 16th, and third on the power play. ... Hall's two assists gave him seven points (five goals, two assists) in the last six games. ... Dallas' Ray Whitney played in his 1,300th NHL game. ... The last time the Stars lost seven in a row was in March 2009. ... Late in the game, Edmonton's Ales Hemsky was hobbling on a swollen ankle. "The early X-ray doesn't show anything, but I think we're going to have to delve a little deeper," Eakins said.