Dvorak scored Arizona's first goal in nearly 190 minutes in the second period and put the Coyotes ahead on a power-play goal with 4 1/2 minutes left.
Kuemper stopped Kevin Shattenkirk on a short-handed breakaway just before Dvorak's second goal and helped Arizona withstand a late power play. Conor Garland also scored in Arizona's second win in six games.
''I thought we had a lot of energy,'' Dvorak said. ''Obviously, we knew it was a big game for us. We didn't want to lose again here at home. We brought everything we had tonight.''
Danton Heinen scored for the second straight game with Anaheim's first power-play goal of the season. Jakob Silfverberg also scored and John Gibson had 31 saves for the Ducks. Two of the three goals allowed by Gibson went off Anaheim players.
''Coaches say it on every team: put pucks on net, puck on net,'' Anaheim coach Dallas Eakins said. ''Get it into that red zone and you're going to get bounces sometimes.''
Arizona managed just 16 shots against Vegas goalie Marc-Andre Fleury on Sunday, but generated 31 against Gibson on Tuesday. None got through, leading to a second straight 1-0 loss.
The Coyotes also had trouble with turnovers the last game against the Ducks, including one that led to the winning goal by Heinen. Silfverberg took advantage of an early one Thursday night, beating Kuemper with a quick shot after Nick Schmlatz couldn't control an ill-advised pass from Jordan Gross between the circles.
Gibson kept the shutout streak going by blocking a shot by Clayton Keller off the post and stuffing Christian Fischer on a late 2-on-1.
The Coyotes dominated the second period - 12-1 in shots - and finally broke their long scoreless streak midway through. Dvorak got it on a shot from behind the goal that hit Anaheim defenseman Kevin Shattenkirk's skate.
It was Arizona's first goal since Jordan Oesterle scored with 59 seconds left of a 5-2 win over Vegas last Friday.
''Whenever you go through a little stretch like that, everyone kind of holds their stick a little tighter, so it's nice to get an ugly one,'' Dvorak said. ''Everyone seems to have a little more confidence and you could see we were all over them.''
The Coyotes needed 52 seconds of the third period to take their first lead in three games when Garland had a shot go off a stick out front after shaking Ducks defenseman Cam Fowler.
Heinen followed with Anaheim's first power-play goal in 18 tries this season, squeezing a shot from the left circle under Kuemper's stick arm on a long rebound.
Dvorak answered with a power-play goal of his own, one-timing a one-touch pass from Phil Kessel in the slot shortly after Kuemper's shorthanded stop on Shattenkirk. Kuemper also had a snatching glove save on Ryan Getzlaf in the second period to preserve Arizona's momentum.
''To be able to not have that much action and then those two grade-A's, that says a lot about good Darcy Kuemper for me,'' Coyotes coach Rick Tocchet said.
LONG DUCK SHIFTS
Anaheim had a good road period in the first, limiting its shifts and creating some good scoring chances.
The Ducks were on their heels in the second period, unable to get out of their own for long stretches. They played better in the third period, but the extra time on the ice took a toll.
''We had a solid first period and then for whatever reason, we went blank in the second,'' Eakins said. ''We got it back a little in the third, but this league is when you only play 40 minutes.''
Coyotes D Niklas Hjalmarsson blocked tied Dion Phaneuf (1,550) for 19th place on the NHL's all-time blocked shots list (since 2005-06). ... Anaheim managed three combined shots in the second period the past two games. ... Dvorak's multi-goal game was his eighth career and first since No. 27, 2019 against Anaheim. ... The Ducks had killed 14 straight penalties before Dvorak's second goal. Anaheim is 24 for 27 on the penalty kill this season.
Ducks: Host St. Louis on Saturday and Sunday nights.
Arizona: At St. Louis on Tuesday night.
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