Doan scored with 30.3 seconds left in overtime, capitalizing on an ugly turnover in the Anaheim zone and giving the Coyotes a 6-5 victory over the Ducks on Wednesday night.
It was a welcome sight for Mueller, a 19-year-old rookie center whose three goals came after a season-opening 12-game stretch in which he scored only once.
"It's an unbelievable feeling," said Mueller, the eighth overall pick in the 2006 draft. "The guys have been laying it out there on a silver platter for me. Tonight I just got the bounces and they went in. I'm playing with guys like Shane Doan and Steven Reinprecht, who are great players. And when they put you on the ice with them, you have to contribute."
Reinprecht had a power-play goal and two assists, helping Phoenix extend its road winning streak to five games. Radim Vrbata scored in his third straight game for the Coyotes, who played the defending Stanley Cup champions for the third time in a span of six games and beat them for the second time.
The game appeared to be heading for a shootout, as Anaheim's Corey Perry was content to skate backward with the puck behind the Ducks' blue line. But he collided with teammate Francois Beauchemin near the left boards, and Doan jumped on the loose puck before beating a stunned Jean-Sebastien Giguere with a slap shot to the glove side for his 36th career game-winning goal.
"It was just a lucky bounce, but you've got to take advantage of it," Doan said. "Obviously, you put your head down and shoot as hard as you can."
Mathieu Schneider had a goal and two assists for Anaheim. Perry, Chris Kunitz and Todd Marchant also scored for the Ducks, who are off to a 6-8-3 start and are still awaiting a decision from Teemu Selanne and Scott Niedermayer as to whether they will come back to the team or retire.
"We've got a lot of new faces and we don't have the same makeup as we had last year," said Chris Pronger, who has replaced Niedermayer as captain. "It's a work in progress and it's going to take time, but we've got to continue to push forward and not let this bother us."
Mueller gave Phoenix a 5-4 lead with 15:45 to play, scoring from the edge of the crease after defenseman Kent Huskins lost the puck to Daniel Carcillo behind the net. The goal came while Perry was serving a high-sticking penalty.
"We're just not sharp in our own end," Pronger said. "We're allowing bad turnovers and not playing our positions, and it's costing us at times with either bad goals or untimely goals."
The Ducks tied it for the third time less than 1 1/2 minutes later as Perry beat Alex Auld to the glove side with a 15-foot wrist shot from the right circle. Auld has allowed nine goals in his last two starts against the Ducks, after beating them 1-0 with 31 saves on Oct. 25 at Anaheim.
For the second straight game, Ducks coach Randy Carlyle pulled his starting goalie in an attempt to keep things from getting out of hand. Ilya Bryzgalov was yanked at 17:11 of the second period after giving up four goals on 18 shots. In Sunday's 5-0 home loss to Dallas, Giguere was benched after surrendering four goals on 19 shots.
"We're a fragile team right now," Schneider said. "I think we showed a lot of character by battling back, but I thought we sat on our heels a little bit too much once we tied it up. It was a crazy game."
After Marchant's first goal of the season gave Anaheim a 2-1 lead at 4:10 of the second period, the Coyotes responded with goals by Mueller, Reinprecht and Vrbata during an 8:46 span. Vrbata's short backhander from just outside the crease gave Phoenix a 4-2 lead, sending Bryzgalov to the bench.
Schneider made it a one-goal difference about 1 1/2 minutes after the change, beating Auld through a screen with a 50-foot slap shot while Mueller was off for hooking.
Miller tied it less than 2 minutes into the third period during a goalmouth scramble. Referee Paul Devorski needed the video goal judge to sort things out, because the NHL eliminated goal judges behind the net this season in order to sell more tickets.
The Coyotes play at San Jose on Monday night, preventing coach Wayne Gretzky and wife Janet from attending longtime teammate Mark Messier's induction into the Hall of Fame at Toronto. "Obviously, we'd love to be there because that night typifies the career he had and all the great memories that we had together as friends and as teammates. But I'll be there in spirit and we'll be watching it on TV," said Gretzky, who won four Stanley Cups with Messier in Edmonton and was inducted into the Hall of Fame in 1999. "We always enjoyed playing with each other. We had fun together, we pushed each other and we made each other better players. And at the end of the day, we both benefited tremendously from that."