"The resiliency of this group is incredible," Tanev said. "We didn't stop pushing. That's the thing."
The fourth line player was undrafted, signed as a free agent and was playing his 15th game.
"This is my first time playing at Joe Louis Arena and to get my first goal and then that," Tanev said. "It's just a great feeling."
Patrik Laine, Mark Scheifele and Nikolaj Ehlers also scored for Winnipeg. Connor Hellebuyck, from the Detroit-area suburb of Commerce Township, stopped 30 shots.
"The players did a great job of shutting the game down in the first period," Jets coach Paul Maurice said. "I really enjoyed this win from a coach's standpoint."
Luke Glendening, Henrik Zetterberg and Justin Abdelkader scored for Detroit, and Petr Mrazek made 26 saves. The Red Wings are 0-3-1 in their last four to drop to 6-5-1.
"You've got to play a complete game in this league. Players are too good and will make you pay if you make mistakes and turn the pucks over," Abdelkader said. "We've got to be better that way but there's lots of things to build off of the last few games. It's a long season. We'll be better and get ready for Sunday (when the Red Wings host the Edmonton Oilers)."
It was Gordie Howe night at Joe Louis Arena. The family of the late Hall of Famer spoke to the media before the game. Howe died on June 10 at the age of 88. His son, Mark Howe, is Detroit's director of pro scouting. The first 5,000 fans received Gordie Howe statue replicas.
Mark and his siblings, Marty, Murray and Cathy dropped the puck for the ceremonial opening faceoff.
Tanev scored the winner on a breakaway, beating Mrazek on the glove side.
Ehlers added an empty-net goal in the last minute. It was his third goal.
Tanev's first goal, with 7:36 left, tied it at 3.
After he beat Mrazek under the crossbar from in close, the puck went in and out so fast play continued for about a minute. After a stoppage, the play was reviewed and called a goal.
Abdelkader gave Detroit a 3-2 lead 9:12 into the third period.
Scheifele tied it at 2 earlier in the third period. It was his sixth goal.
"I thought we started really well. Even in the second it felt like we carried the play at times. Then in the third for whatever reason, I thought we fell back a little bit," said Detroit defenseman Niklas Kronwall, who made his season debut after being bothered by a sore knee, "In saying that, I don't know how many great scoring chances they had. But they came out winning. Two points are what you need and we didn't get that."
Zetterberg gave the Red Wings a 2-1 lead 9:40 into the second period. He batted the rebound of Tomas Tatar's shot out of the air and into the net.
The goal was originally waved off because it was first indicated that Zetterberg's stick was higher than the crossbar. But referees Chris Lee and Ghislain Hebert and linesmen Tim Nowak and Ryan Galloway huddled and immediately reversed the call. The call of a goal was then upheld by the NHL Situation Room in Toronto.
Glendening gave Detroit a 1-0 lead 3:04 into the game when he deflected Dan DeKeyser's shot/pass from the left point past Hellebuyck. It was Glendening's first goal of the season.
Laine tied it at 1 with 4:30 left in the first period. He leads NHL rookies with seven goals.
NOTE: Detroit D Niklas Kronwall made his season debut. He missed the first 11 games of the season because of knee pain. ... Winnipeg was without LW Drew Stafford (upper body), D Tyler Myers (lower body) and D Mark Stuart (lower body). ... The Red Wings were missing LW Thomas Vanek (hip). ... It was the second of back-to-back games for the Jets. They lost 4-3 in overtime to the Washington Capitals on the road Thursday night.