Terry, who had a three-point night, fired a pair of goals and an assist.
Ryan picked up the disc just outside the Ducks crease and skated it to the top of the faceoff circle before snapping a low wrister just inside the post to give Anaheim the win.
Leo Carlsson also scored for the Ducks.
Radko Gudas had a goal and an assist for Anaheim.
John Gibson made 27 saves for the Ducks, who won their third straight game to move to within a game of .500 (16-17-4).
Mark Scheifele and Adam Lowry scored for Winnipeg, who lost their second straight.
Alex Iafallo had a goal and an assist for the Jets.
Connor Hellebuyck turned aside 20 shots, who dropped to 27-11-2.
Mark Scheifele scored 33 seconds into the contest after Gabriel Vilardi stripped the puck off Radko Gudas in the corner and got slid the disc to Kyle Connor who was cutting in front of the Anaheim net.
Connor fed Scheifele a nifty backhand pass which he slid into a wide open net.
The goal was his 23rd of the season.
Adam Lowry gave Winnipeg a two-goal lead 17:17 into the first when he finished off a two-on-one with Alex Iafallo, burying his feed with a low blocker side wrister just inside the post.
The goal was his 10th of the season.
Leo Carlsson tipped a Radko Gudas shot from the point past Hellebuyck with just over a minute left in the first period to get Anaheim on the board.
The goal was his 8th of the season.
Troy Terry knotted the game at two when he one timed a Ryan Strome feed from the right face off dot just under seven minutes into the second period.
The goal was his 12th of the season.
Alex Iafallo gave the Jets the lead 17:16 into the third when he scored on a wraparound.
The goal was his 6th of the season.
Radko Gudas tied it up at 18:10 on a slapshot from the point to make it 3-3.
The game went into overtime.
Troy Terry fired the game winner 3:34 into the extra frame.
Anaheim visits Edmonton Friday while Winnipeg hosts Detroit on Saturday.
SHOTS-ANAHEIM 24 WINNIPEG 30
ATTENDANCE-15,225
