"Don't quit until there's 27 up and 27 down," Detroit outfielder Curtis Granderson said.
With the Tigers down 6-5 in the seventh, Brandon Inge led off with a single off reliever Jose Arredondo (7-2). Granderson tripled to tie the game and Polanco followed with a single to put Detroit on top.
Hessman added his first homer of the season in the eighth.
"We kept battling. It kept going back and forth," Hessman said. "Every time they got up, we came back and scored."
Mark Teixeira had three hits, including a homer, and three RBIs for Los Angeles, which saw its magic number to clinch the AL West remain at eight.
"Those guys [Rodney, Farnsworth] can get the key strikeout when they need it and that's what they did," Angels manager Mike Scioscia said.
Teixeira made it 2-1 in the fourth with his ninth home run.
Gary Sheffield's two-out RBI single in the fourth restored the Tigers' two-run lead.
But the Angels scored four in the fifth to take a 5-3 lead. Brandon Wood doubled in a run, Sean Rodriguez's sacrifice fly tied it at 3, and Chone Figgins' fielder's choice grounder made it 4-3. Teixeira's two-out RBI single made it 5-3.
Polanco's two-run double in the fifth tied it.
"Just compete, compete, compete," he said.
Teixeira's RBI single in the seventh gave Los Angeles a 6-5 lead.
Detroit starter Zach Miner allowed five runs and eight hits in six innings.
Los Angeles' Jon Garland gave up five runs and seven hits in six innings.
"I put my team in a hole early, they got me four back and I gave the right back," Garland said. "Just a bad game."
The start of the game was delayed 1 hour, 14 minutes by rain. ... Teixeira was the DH. He didn't play 1B because of Granderson's hard grounder that went off his hand in Tuesday night's game. Scioscia said he expected Teixeira to be back at first on Thursday. ... Detroit SS Edgar Renteria was ejected by home plate umpire Chris Guccione after striking out in the sixth. ... Angels RHP Jered Weaver's scheduled Friday start was pushed back to Monday because he cut his hand on one of the benches in the dugout before the game. RHP Dustin Moseley will start in Weaver's place Friday. ... Cabrera was walked intentionally in the fourth and fifth.