Larkin cut it to 2-1 at 7:35 of the second period, beating Kuemper with one second left on a power play.
Hinostroza's goal made it 3-1 at 4:37 of the third, With Howard on the other side of the net, Detroit forward Tyler Bertuzzi skated over to make the save on Hinostroza's initial shot, but the puck deflected into the slot and Hinostroza scored on a backhand.
The arena horn sounded before Hinostroza scored, but the goal was upheld because neither referee blew his whistle to stop play.
"I haven't seen that very often, if ever in my life. The horn went, the lights flashed, (but) the referee never blew the whistle. In the end, the referee said basically that until the whistle ends the play, play continues," Detroit coach Jeff Blashill said. "It's unfortunate, but we didn't play well enough (to win)."
Kuemper has won seven consecutive starts, allowing two goals or fewer six times, He is 15-4-4 since Jan. 1. The Coyotes, who haven't reached the playoffs since 2012, are 4-0-0 on a seven-game homestand and have won nine of their past 11.