"The No. 1 line is dangerous right now because of their skill and chemistry," Stars coach Marc Crawford said. "They're a confident bunch."
Eriksson, Richards and Neal have combined for eight goals and nine assists in their last three games.
Brenden Morrow added his 200th career goal, Jamie Benn also struck on the power play, and Mike Ribeiro had three assists for Dallas. The Stars set a season high for goals and have 15 in their last three games.
The Stars failed to capitalize on their first two power-play chances, but they remained persistent.
"We're trying to shoot it more and we're finding ways to get in front of the net," said Eriksson, whose four points were a career high. "That's huge for us. We need the power play to work. We got a little frustrated, but we were able to get the power play working and that's why we won the game."
Kari Lehtonen stopped 25 shots as the Stars won their third in a row after dropping the first three of a season-high six-game homestand.
Eriksson's power-play deflection off Ribeiro's pass at 15:44 was the only goal of the opening period.
Richards made it 2-0 at 3:22 of the second period, converting Neal's cross-ice setup from low in the left circle, and Richards' second of the game at 5:21 of the second period extended Dallas' lead.
At that point, Tippett replaced starting goalie Ilya Bryzgalov with Jason LeBarbera, making his third appearance of the season. Bryzgalov stopped 15 of 18 shots.
The Coyotes were in catch-up mode for most of the night. Phoenix also got some bad bounces on Dallas goals that caromed in off Coyotes.
"It's disappointing," Tippett said. "We got behind early and they got some breaks on some pucks that bounced off our guys and into the net, and we couldn't create the breaks ourselves. But when a team gets those breaks, they earn them and their group found a way to get it in the net."
Phoenix cut it to 3-1 at 13:34 of the second on a goal that was credited to Lepisto but the puck appeared to go in off the skate of Dallas defenseman Mark Fistric.
Power-play goals by Benn and Eriksson during a 1:09 span of the second period gave Dallas a four-goal edge.
"Our power play stuck with it," Crawford said. "We had people around the net and when you do that, the rebounds fall to you. We did a good job of capitalizing."
Doan's power-play goal at 2:28 of the final period - his first of the season - and Korpikowski's goal with 3:02 left made the score more respectable.
- Phoenix is without D Kurt Sauer (head injury).
- Texas Rangers manager Ron Washington, wearing a warmup with a World Series logo, dropped the ceremonial first puck and received a nice ovation. Rangers pitcher Derek Holland also attended the game.
- The Coyotes won two of three in Dallas last season.
- The Stars have their second three-game winning streak of the season. Dallas failed to string together three straight victories all of last season.