Derek Armstrong had a goal and an assist and Rob Blake scored on a power play for the Kings, who ended a four-game losing streak after outshooting Phoenix 7-0 in overtime.
Los Angeles goalie Barry Brust, who made his NHL debut at Phoenix on Nov. 30, stopped 28 shots in the rematch and all three he faced in the shootout. Kings coach Marc Crawford gave Brust the nod after Dan Cloutier allowed 15 goals over the previous three games.
Fredrik Sjostrom and Oleg Saprykin scored 77 seconds apart in the third period, Yanic Perreault had a goal and an assist and Owen Nolan had two assists for the Coyotes. Tellqvist made 34 saves after stopping 29 shots in Saturday's 2-0 victory over the league-leading Anaheim Ducks.
The Kings tied it when Michael Cammalleri batted down a fluttering puck and passed it to Kopitar at the right side of the net. The rookie then fed the puck blindly between his legs into the low slot, and Avery was there to sweep it past Tellqvist's stick for his seventh goal.