Loui Eriksson scored twice to lead the Stars to a 3-2 victory Saturday night.
"It's good for the confidence to get this win," said Mike Ribeiro, who had three assists. "We played much better defense and when you focus on defense, you have a better chance to win."
The Stars won in Phoenix for the 10th time in the last 14 meetings in the desert.
"This is the kind of effort from which we can build," Stars captain Mike Modano said. "We're noted for playing good defense and, if you're playing that game at its peak, we're a tough team to beat."
"We didn't fire on all cylinders," Phoenix coach Wayne Gretzky said. "We had one line and one player playing well, and didn't have enough out of everybody."
Eriksson also had a two-goal game against the New York Islanders on Oct. 23.
Eriksson scored his first goal on a backhander with 2:54 left in the opening period. Rushing down the right wing, Eriksson converted a pass off the boards from Ribeiro into his seventh goal of the season.
The lead could have been larger, but Phoenix killed off a double-minor to Olli Jokinen for high-sticking just 30 seconds into the game.
The Coyotes evened matters when Reinprecht scored at 2:32 of the second period. Reinprecht used Kyle Turris, just outside the crease, as a decoy and then slid the puck behind Turco for his third of the season.
Tied for 22nd in the NHL in power-play goals, the Stars went ahead with the man advantage. Parrish scored his third-power play goal, and fourth of the season, when he tipped in Sergei Zubov's shot from the blue line at 8:13 of the middle session.
Eriksson picked up his second of the game when he scored off a goalmouth scramble with 55 seconds left in the second period.
Phoenix came back 16 seconds later when the rookie Porter, last season's college player of the year at the University of Michigan, converted a centering pass from Mikkel Boedker into his third of the season.
The Coyotes had an opportunity to tie it late. The Stars' Steve Avery was whistled for a holding minor at 12:45 of the final period, but Phoenix failed to convert.
In the final seconds, Turco robbed Jokinen in close on a set-up from Reinprecht.
"It was a bang-bag play," Reinprecht said. "The puck slid through a few guys to Olli and [Turco] made a great save. Another inch to the left and it's in, but that's the way it goes."
Modano needs six points to reach 1,300 in his 19-year NHL career. He would be the 31st player in league history to reach this level. ... Ribeiro had his second three-point game of the season.... Phoenix has lost two straight after winning three in a row.