Donskoi scored his second goal of the game with San Jose goalie Aaron Dell pulled for an extra skater after Arizona scored twice earlier in the period. Vlasic then got his fifth of the season with an assist from Joe Thornton, who had a goal and two helpers to move ahead of Hall of Famer Adam Oates for 17th on the career scoring list (1,420 points).
Joe Pavelski and Logan Couture also scored for San Jose, and Dell stopped 13 of 15 shots after replacing Martin Jones in net.
Arizona got goals from Derek Stepan, Alex Goligoski, Christian Fischer, Oliver Ekman-Larsson and Josh Archibald. Scott Wedgewood made 38 saves.
Thornton opened the scoring at 5:53 of a frantic first period in which the teams combined for six goals. Pavelski and Couture also scored then for San Jose, while Stepan, Goligoski and Fischer combined to make it 3-3 at the first intermission.
Donskoi scored his ninth of the season late in the second period, but then Ekman-Larsson and Archibald scored early in the third to make it 5-4 Coyotes.
NOTES: Arizona has lost five of six. ... Thornton has 85 points against the Coyotes in 22 games, more than he has against any other team. ... Arizona F Zac Rinaldo was back in the lineup for the first time after a six-game suspension for a blindside punch to Colorado's Samuel Girard. Coach Rick Tocchet scratched C Nick Cousins to make room for Rinaldo. ... San Jose F Mikkel Boedker, a healthy scratch in the team's last game before its break on Jan. 7, was back in the lineup. ... D Dylan DeMelo, out with flu symptoms, is expected to come off injured reserve for Monday's game against the Los Angeles Kings.
Coyotes: Host the Sharks on Tuesday night.
Sharks: Play at Los Angeles on Monday.
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