Chris Kunitz and Kris Letang each added a goal and an assist and Matt Cullen also scored for the Penguins, who have won three of their last four.
Hornqvist opened the scoring at the 5:42 mark in the opening period by stuffing in his own rebound. Kunitz forced a turnover and got the puck to Crosby, where the Penguins captain fed the puck to the crease. Hornqvist battled for the puck before getting it on net, then backhanded the rebound past Coyotes goaltender Louis Domingue.
Hornqvist doubled the lead near the end of the period when he redirected a shot from Kunitz into the net.
Kunitz made it 3-0 in the second period when he deflected a Letang shot from the point for his 12th of the season. Crosby assisted on all three goals.
Four minutes later Hornqvist completed the hat trick—his first in the NHL—with one-timer on a wrist shot during a Penguins power-play to put the home team comfortably in front 4-0. Malkin and Phil Kessel earned assists.
Letang and Cullen then scored 16 seconds part to open the third period and the rout was on.
Fleury, who is 11-3-1 in his last 14 starts, earned his fifth shutout of the year.
Russian forward Sergei Plotnikov, who was traded from the Penguins to the Coyotes on Monday morning, skated on the fourth line for Arizona. The Penguins also dealt prospect Matia Marcantuoni to the Coyotes for former Penguins forward Dustin Jeffrey, as well as Dan O’Donoghue and defenseman James Melindy.
The Penguins travel to Eastern Conference-leading Washington on Tuesday night, a makeup game after their scheduled Jan. 24 meeting was postponed following a major snowstorm.