Anaheim, which averaged the fewest goals in the NHL last season (2.21), has scored at least three in 10 of its 12 games.
"We're playing in the offensive zone," Ducks captain Ryan Getzlaf said. "We're putting the puck in the net when we've got the chances."
Shayne Gostisbehere scored, and Karel Vejmelka made 28 saves for the Coyotes.
"Mentally, we had a lack of urgency," Tourigny said. "I understand we're in a tough situation, but nobody will feel sorry for ourselves, so we need to show more character in our situation."
Henrique scored 34 seconds into the first period to give Anaheim a 1-0 lead. Getzlaf attempted a centering pass to Troy Terry, but the puck ricocheted off the skate of Arizona defenseman Jakob Chychrun and banked off the end boards to Henrique at the right post.
With an assist on the play, Terry extended his point streak to 10 games (seven goals, six assists).
"Troy's playing great right now," Getzlaf said. "He's skating off the puck very well and we've developed some of that chemistry where I kind of know where he is. Obviously, he has an ability to finish, so it's been great."
Sonny Milano made it 2-0 at 18:13, scoring on a one-timer off a quick setup down low by Henrique on the power play. It was the 11th power-play goal of the season for the Ducks, who scored 11 in 56 games last season.
Sam Carrick
pushed the lead to 3-0 when he redirected a feed from Derek Grant at 9:46 of the second period.
"I felt for the first time this year we got outworked in the second period," Tourigny said. "That's unacceptable. That's not who we are."