Melbourne led by a point when Kate Hore snapped a goal with nine minutes remaining in Sunday's match at Fremantle Oval.
But a major on the run from Ange Stannett proved the winning moment for Fremantle as they held on for the 6.4 (40) to 5.5 (35) triumph.
Dockers star Bowers was the pivotal figure in the match, racking up 14 disposals in the fourth quarter alone to ensure Melbourne left Perth empty handed.
Bowers finished with 27 disposals, 17 tackles and four clearances, while Gabby Newton (29 disposals) and Aisling McCarthy (29 possessions, five clearances, one goal) were also huge.
Star Dockers forward Tighe, playing her first match since recovering from a third knee reconstruction, kicked a team-lifting goal in the third quarter but was taken out of the game a short time later with a knee issue.
Fremantle weren't immediately sure whether Tighe had suffered a fresh injury concern.
"The only thing I've got from this is it's knee soreness," Fremantle coach Lisa Webb said.
"She's a terrific person, she doesn't give much away. I honestly don't know enough.
"Hopefully she's fine. I mean, she worked incredibly hard to get back to where she is, and she's an important player for us.
"No matter what happens, we'll wrap our arms around her."
Fremantle (4-5) kept their slight finals hopes alive with arguably their gutsiest display of the season, while Melbourne (7-2) slipped to third on the ladder.
Melbourne lost Georgia Gall to a painful right ankle injury early in the match, while Demons star Tayla Harris was cleaned up in the dying moments when she collected by Mim Strom as the Fremantle ruck reached out after a ground ball.
The Dockers stunned Melbourne early with goals to McCarthy, Georgie Brisbane and Laura Pugh, giving the home side an 18-0 lead inside 12 minutes.
Melbourne kicked three goals to none in the second quarter to turn momentum their way, with Alyssa Bannan's goal on the run sparking the visitors.
Melbourne blew a series of chances in the third quarter, and were made to pay at the other end when Tighe kicked the only goal of the term.
The last quarter was a war of attrition, and it was Bowers who stood the tallest.
