Turris moved in wide and beat Jets goaltender Connor Hellebuyck with a wrister just inside the far post.
The win moved the Pacific division leaders to 12-4-0 on the season.
The Jets, who have now posted points in their last 11 games, dropped to 9-4-3.
Connor McDavid Edmonton's lone goal in regulation.
The goal extened his point scoring streak to 16 games, the third longest in Edmonton Oilers history.
Stuart Skinner picked up the win for the Oilers, who rebounded after dropping a 5-2 decision to the Jets on Tuesday night.
Connor Hellebuyck made 31 saves for Winnipeg.
There was no scoring through two periods.
Nikolaj Ehlers scored just under the 14 minute mark of the third period, taking a backhand saucer pass from Mark Scheifele before firing a rocket past Skinner, beating the Edmonton netminder high glove side to give Winnipeg a 1-0 lead.
The goal was his 5th of the season.
Connor McDavid replied 28 seconds later with a spectacular individual effort, moving past Logan Stanley before firing a wrister just inside the left post.
The goal was his 11th of the season.
The game went to overtime.
There was no scoring in overtime and the game went to a shootout.
Edmonton-Draisaitl (miss), McDavid (score), Turris (score) Winnipeg-Connor (miss), Scheifele (miss) The Jets travel to Vancouver for a Friday night matchup while Edmonton hosts Chicago on Saturday.
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