Vernon Fiddler's chip popped into the air at the top of the crease, where it hit the shaft of Jovanovski's stick and went past goalie Chris Mason.
"It was a good effort by Fids," Jovanovski said. "He kind of threw it to the net and the rebound came up the gut there. I just charged the net and it was high, but it happened to hit my shaft and go in."
Officials reviewed the play for several minutes as players waited on the ice and the fans chanted "Goal! Goal!" before it was ruled a score.
"It just went up in the air and I saw him barreling in," Mason said. "I don't know what he got it with, but he must have gotten it with some legal part of his body. I was hoping he gloved it in or was in the crease, but that wasn't the case."
Phoenix's Scottie Upshall sent the game to overtime, capping a 2-on-1 break with a wrist shot just inside the far post with 11:33 left in regulation.
"He [Matthew Lombardi] put it right in my wheelhouse, right where as a goal scorer you like to shoot it," Upshall said. "They say good teams find a way to win. Tonight that bounce in overtime helped us."
Shane Doan also scored to help the Coyotes win their second straight game.
"I said it was going to be an ugly one and it was," Doan said.
"We had multiple opportunities to score in the second and came out of there with a 2-1 lead," Blues coach Andy Murray said. "We tried to be assertive but their team's playing well right now."
Kariya's goal wasn't artistic, but it was unique.
With the game tied at 1, Coyotes defenseman Keith Yandle started skating out from behind the net to the right of goalie Ilya Bryzgalov. But Kariya shot the puck off Yandle's stick blade with a backhand sweep, beating Bryzgalov at 12:19 of the second.
"Obviously Yandle isn't feeling good about that one but it's forgotten because the guys picked him up," Coyotes coach Dave Tippett said. "It was kind of a roller-coaster game."
Backes opened the scoring at 3:22 of the second while the Blues were awaiting a delayed penalty after B.J. Crombeen was cross-checked into the Coyotes' net. Crombeen scrambled clear of the crease seconds before Backes blasted a shot from the point.
Doan tied it at 9:24 of the period when he collected a rebound of Adrian Aucoin's long shot off the end boards to the left of the crease and scored on a quick wrist shot. The goal snapped Phoenix's scoreless streak of 166 minutes, 47 seconds dating to Oct. 8 in Buffalo.
Bryzgalov, who posted a 137:46 scoreless streak before Backes' goal, made 22 saves for the Coyotes.
There were approximately 5,000 fans in attendance, below the 6,899 official attendance figure given by the team that includes unused season tickets. ... LW Taylor Pyatt made his season debut after missing Phoenix's first five games because of a lower-body injury. ... Doan has 16 goals and 26 assists in 55 career games against the Blues. ... Kariya's goal was only the second even-strength score against Bryzgalov this season.