Kostitsyn, shooting first for the Preds, beat Mike Smith through his legs for the win.
"I try to do my best move to score in practice and then try the same thing in the shootout," he said. "We don't play many games against Phoenix so I don't know the goalie. I try to do many different moves in practice, and (Monday night), I did the wrist shot and scored."
Despite giving up the four goals, Nashville goalie Pekka Rinne, who leads the NHL in wins, was strong down the stretch and to keep the Predators in the game.
"It was a little disappointing to give up the two late goals, but we managed to get two points and that's the important thing," Rinne said. "It may not be so good when a team comes from behind like that, but with the win, you feel fine."
Erat opened the scoring when his shot from the right faceoff circle trickled through Smith's pads with 29 seconds left in the opening period. He helped set up second-period goals by Mike Fisher and Francis Bouillon.
Craig Smith added his 15th early in the final period to give Nashville a 4-2 advantage. Then the Coyotes responded.
Ekman-Larsson scored at 7:11 to get Phoenix within one, and Torres tied it with 4:59 left when he poked in a goalmouth scramble.
The Coyotes recorded one point and remained in seventh in the Western Conference. Colorado beat Anaheim in overtime earlier Monday and is one back of Phoenix with 78 points.
"At this point in the season, you take every point you can," Phoenix coach Dave Tippett said. "We had to rally because we made poor mistakes. These are mistakes which cannot happen at this time of the year."
Nashville pulled within two points of Detroit for fourth place in the West.
Phoenix tied it twice in the second. Daymond Langkow tipped in Ekman-Larrson's shot from the right point 49 seconds into period. After Fisher scored, Keith Yandle drilled a 25-foot slap shot past Rinne at 14:23.
Bouillon then knocked in his own rebound with 1:34 left in the second to make it 3-2.
Smith and Rinne finished with 31 saves apiece.
"We showed some resilience as a group," Phoenix captain Shane Doan said. "We had some big goals late in the third and tied it up. It's a big point but obviously no one is happy."
Erat picked up his second three-point game of the season. ... Langkow's goal was just his second in his last 21 games. ... Nine of Nashville's final 13 games are on the road, while Phoenix has five of its next six on the road.
Copyright by STATS LLC and The Associated Press
GLENDALE, AZ - MARCH 12: Shane Doan #19 of the Phoenix Coyotes greets fans as he heads to the locker room after...