The Predators, who snapped a two-game losing streak, leapfrogged idle Detroit into first place in the Central Division and the Western Conference. They did it despite not getting any points from new forward Peter Forsberg for the second straight game since he joined Nashville.
Jean-Pierre Dumont and Jason Arnott also scored for Nashville, who are tied with Buffalo for the overall lead in the NHL with 83 points.
Oleg Saprykin scored Phoenix's lone goal.
Dumont scored at 18:49 of the first period when he was awarded a penalty shot after being taken down from behind by Ed Jovanovski on a breakaway. Dumont skated in and beat goalie Curtis Joseph with a shot high over the shoulder to the stick side.
Just 39 seconds into the middle period, Steve Sullivan skated down the left side and fired a shot that bounced off Joseph. Dumont tried to shoot the rebound, but the puck trickled off his stick. Arnott finally hammered the loose puck home.
Hartnell then turned it on, twice getting ahead of the defence.
On the first at 5:34 he was all alone when Kimmo Timonen hit him with a long pass that he shot between Joseph's skate blade and the right post.
It took only 23 more seconds for him to get alone again. David Legwand found him with a pass and Hartnell beat Joseph low to the stick side.
Saprykin ruined Tomas Vokoun's shutout bid with 2:46 remaining in the game, tipping in Keith Ballard's shot from just inside the blue line.
Notes: Nashville LW Paul Kariya played in his 800th NHL game. The Predators are 6-6 since the all-star break. Joseph had allowed only 2.83 goals per game in his previous seven outings. ... The Predators are 31-8-1 when scoring first. ... Legwand's 49 points (20 goals, 29 assists) are a career high. ... Jovanovski left the ice at 14:01 of the third period after taking a puck to the face.