Keith Yandle, Raffi Torres and Derek Morris scored and Ray Whitney added a pair of helpers for the Coyotes, who have won three straight games. Mike Smith was solid in net, making 28 saves in the victory.
"That's three games now where we've played how we have to play," Coyotes head coach Dave Tippett said. "We have a lot of people that are committed to doing things that make you win hockey games."
Michael Ryder scored for the Stars, who were unable to carry momentum from a 2-1 shootout victory over the Minnesota Wild on Saturday. Kari Lehtonen was tagged for all four goals on 24 shots in defeat.
Vrbata's go-ahead goal came at 14:30 of the second stanza after the puck found its way to Rostislav Klesla in the left circle. Klesla fed a cutting Vrbata, who tapped it into the net from in front to put the Coyotes ahead, 2-1.
The Coyotes put the game away with a pair of goals in the third period.
The first tally of the stanza came off the rush at 5:41 when Mikkel Boedker accepted a long cross-ice pass in the neutral zone and gained the offensive blue line with speed. Boedker drifted to the circle and sent a quick pass to Torres, who took a quick touch to control the puck and ripped it high over the shoulder of Lehtonen for a 3-1 Coyotes lead.
Morris capped the scoring with 3:51 to play when he pounced on a loose puck in the slot and wired a slap shot by Lehtonen.
"Awful, atrocious," Stars defenseman Sheldon Souray said of his team's performance. "We've gotten by on a really good goaltender, but it's not good enough."
The Coyotes struck first at 4:43 of the first stanza when Yandle ripped a slap shot from the point that got through traffic in front and past Lehtonen.
Dallas responded to tie it up 2:34 into the second stanza as a result of a fantastic individual effort by Ryder.
Holding the puck in his defensive zone, Ryder started up the ice looking for a breakout pass, but he gained speed through the neutral zone, stick-handled his way around a couple Coyotes defenders and let a quick wrister go that beat Smith low to the far side.
Tuesday marked the fourth meeting of the season between the teams. The season series is now tied at two...It was Morris' first goal since March 24, 2011, snapping a 51-game goalless drought...Dallas could not score on four power play opportunities, while the Coyotes went 0-for-1 with the extra man...Dallas will visit the Columbus Blue Jackets on Thursday, while the Coyotes will host the Calgary Flames, also on Thursday.