Jakub Vrana scored his third goal in two games in the first period and Matt Niskanen had one on his birthday in the second. Pheonix Copley turned away numerous good chances while making 27 saves, and Burakovsky scored the winner with 4:42 left on a shot that caromed off goalie Adin Hill's blocker.
Alex Ovechkin added an empty-net goal after becoming the fastest player — ninth overall — to have 5,000 career shots, reaching the mark in 1,031 career games. Marcel Dionne was the previous fastest at 1,215 games.
"We've been creating chances every game, playing good games, so it's good to see it pay off," Vrana said.
Christian Fischer scored in the first period, but the Coyotes missed on several opportunities to stretch the lead. Lawson Crouse scored in the second and Arizona again wasted some decent chances in the third before Burakovsky scored.
Hill stopped 26 shots, giving up one more goal than he had while opening his Coyotes career with four straight wins.
NOTES: Wilson did not play due to a concussion sustained Tuesday against Vegas. Arizona lost for the third time in 15 games (11-3-1) when scoring first. Niskanen turned 32. Coyotes C Vinnie Hinostroza went out in the first period with a lower-body injury and did not return.