Stempniak scored three goals for his first NHL hat trick, and the Coyotes held on to beat the Los Angeles Kings 4-2 in front of an announced crowd of only 6,706 on Thursday night.
"To do that, win and help the team in a pretty big game is a great feeling," Stempniak said. "This was a big game for us in terms of establishing our identity."
Hanzal sat out with a lower-body injury, and Doan served the first game of a three-game suspension for his hit Sunday on Anaheim's Dan Sexton. Stempniak and Andrew Ebbett, who had been recalled from San Antonio of the American Hockey League to replace Hanzal, provided the offense in their absence.
"The one thing the coaching staff came back to was this would have to be a collective effort," Coyotes coach Dave Tippett said.
Phoenix had dropped three straight after a season-opening victory over Boston in the Czech Republic. All four games had been back-to-back sets, leaving the Coyotes home to watch more hockey than they have played.
"We had no choice but to get two points," said defenseman Ed Jovanovski, who had three assists. "We've got to find ourselves climbing up the ladder and not playing catch-up through these months."
Wayne Simmonds scored his first two goals for the Kings, whose two losses this season have come on the second night of back-to-back games.
Simmonds cut the Kings' deficit to 3-2 with 2:41 left in the game, scoring on a rebound after Brad Richardson's shot was tipped back to him just outside the crease.
But Stempniak scored an empty-net goal from center ice with 34.6 seconds remaining to finish his hat trick.
Los Angeles also was missing a key player. Kings defenseman Drew Doughty sat out because of the upper-body injury sustained Wednesday against Carolina.
"We have to be more accountable to each other as a team," Simmonds said. "That's how we're going to cover his spot."
Stempniak scored his first of the season at 4:30 of the opening period when he redirected Jovanovski's blast from the right point past goalie Jonathan Quick. Stempniak started the play with a shot from the right circle that Quick deflected to the left circle before Jovanovski cycled the puck back to the blue line.
"I didn't even know that first one hit me," Stempniak said. "I guess I have to buy [Jovanovski] a beer or dinner or something."
Stempniak made it 2-0 at 7:24, backhanding a rebound of Taylor Pyatt's shot from the bottom of the left circle over Quick's shoulder.
"The first period is where it's at in the NHL," Kings coach Terry Murray said. "You get yourself in a hole by getting down in the goal department and you're killing off three power plays on top of that. That's hard to dig out of."
Ebbett extended the lead to 3-0 at 5:49 of the second, charging into the Kings zone on the right side of a 2-on-1 break and shooting between Quick's pads for his first goal with the Coyotes.
Doan had played in 193 consecutive regular-season games, dating to Feb. 11, 2008. Doughty had played in 126 straight, dating to Jan. 17, 2009. Coyotes LW Ray Whitney returned to the lineup after missing consecutive games with an upper-body injury. Brayden Schenn assisted on Simmonds' first goal for his first NHL point.