Hiller made 28 saves in his 13th straight win, the NHL's longest streak since Detroit's Chris Osgood did the same in 1996. Only seven other goalies in league history have won 13 in a row.
"It's definitely a great thing, but at the same time I'm really excited about winning with the team," he said. "The personal things kind of put the cherry on the cake."
"If you're winning, you really feel good about yourself and you kind of want to keep that feeling," Hiller said. "Here everybody goes out believing that we can beat anybody in any stadium."
The Ducks improved their NHL-best record to 34-8-5 and 73 points. Phoenix has lost four of five.
"Right now we aren't very good," Coyotes captain Shane Doan said, "and we haven't been very good for a while."
Vatanen started Anaheim's second-period barrage with a slap shot from the right point that slipped through Greiss' legs to make it 2-1 with 14:16 left. Penner netted the next one, with a slap shot off a pass from Perry with 10:49 remaining. Getzlaf then got to a loose puck in the crease and scored to make it 4-1 with 9:05 to go.
"It was a good flurry," Ducks coach Bruce Boudreau said. "Once we got the second goal, which might have been a little bit soft, I thought it sort of energized the team. Then we came on, and get the third and you get the fourth. Things were going pretty smoothly there for a while."
That was it for Greiss. Smith came on and gave up one goal in the third period. Lindholm scored a power-play goal with a shot that hit the camera just inside the net to put the Ducks ahead 5-1.
Hanzal scored with Phoenix on a 5-on-3 advantage, and Ribeiro added a final goal long after the game's outcome had been determined.
That gave Boudreau something to complain about -- "a sloppy finish."
Boudreau said Hiller might be back in goal Sunday night in Detroit.
"I'll talk to the goaltending coach on the plane," Boudreau said. "We'll talk to Hilly and see how he feels, and then we'll make a decision."
Phoenix took a 1-0 lead 3:57 into the game. Korpikoski's shot from in front of the net was deflected by Hiller, but the puck came right back to Korpikoski, who knocked it in for his seventh goal of the season.
It was the fifth time in six games that Anaheim had allowed the first goal, and the Ducks have won all five.
Greiss made a diving stop of Nick Bonino's shot but left the net open behind him. Lindholm, who had just three goals for the season before Saturday, got the deflection and scored to make it 1-all with 7:33 left in the first period.
Phoenix was outscored 9-4 in consecutive home losses to Minnesota and Anaheim.
"We're not a very cohesive group right now," coach Dave Tippett said. "When you chase games all the time, you look like an out-of-sort group, and that's where we are."
Getzlaf left in the second period because of a lower-body injury and didn't return. X-rays were negative. ... Anaheim has scored a combined seven goals in the second period in its past two games, including four at Nashville on Thursday. ... Smith was benched after Phoenix won only three times in his past 17 starts.