The game featured another pressure-packed pitchers' duel, with Detroit's Justin Verlander and Boston's John Lackey holding their opponents scoreless until Napoli's crushing blow with one out in the seventh off a 96 mph (154 kph) fastball.
It was a flashback moment for Napoli, who had hit a home run in his first major league at-bat as a 2006 rookie against Verlander - and none against the hard-throwing righthander since - until Tuesday's game-winning blast.
"He's tough. He was on his game tonight and keeping us all off balance," Napoli said about Verlander, who did not yield a hit until two outs in the fifth inning. "I got him into a 3-2 count and put a good swing on a pitch and was able to get it."
Pressed further about his approach, the heavily-bearded Napoli revealed a superstitious moment with another of his hirsute team mates.
"I rubbed my bat on Jonny's (Gomes) beard before I went out to that at-bat," said Napoli. "I just tried to put a good at-bat together and I came through."
Detroit threatened in the seventh and again in the eighth, with runners on first and third and one out, and the dangerous, though hobbled, Miguel Cabrera at-bat.
Reliever Junichi Tazawa struck out Cabrera, who has been suffering from a groin injury, on an outside fastball before Red Sox manager John Farrell summoned closer Koji Uehara to face Prince Fielder.
Uehara struck out Fielder on a diving, split-fingered fastball to end the threat before shutting the Tigers down in the ninth to seal the victory and get hoisted up over David "Big Papi" Ortiz's shoulder in celebration.
The game was delayed 17 minutes before the bottom of the second due to a power failure, but Napoli supplied the necessary jolt of power for the Red Sox to push ahead in the pivotal game.
Boston starter Lackey went 6-2/3 innings, giving up four hits and no walks, while striking out eight, before giving way to Craig Breslow, who preceded Japan's Tazawa and Uehara in the eighth.
Verlander pitched eight innings, giving up one run on four hits with one walk and 10 strikeouts.
"This series has been marked by very good pitching on both sides," said Boston manager John Farrell. "Tonight, John Lackey was outstanding."
Farrell also saluted his bullpen.
"Bres comes in, picks him (Lackey) up ... then the two key strikeouts in the eighth inning with Junichi against Cabrera, and then Koji against Fielder," Farrell said.
"We liked the match-up against Cabrera with power," he said about going with hard-throwing Tazawa to face the Tigers slugger.
"It was pivotal moment. You're getting the best guy in baseball at the plate, trying to preserve a one-run lead. That was a swing moment for sure."
Detroit manager Jim Leyland could only shrug his shoulders about coming so close to tying or taking the lead in the eighth inning before a roaring crowd at Comerica Park.
"That's just part of the game," said Leyland.
"You don't do it every time. You've got to give the pitcher credit. He won the battle.
"One swing of the bat. They hit it over the fence and we didn't."
Game Four is scheduled for Wednesday in Detroit with Doug Fister, 14-9 in the regular season, expected to start for the Tigers against Jake Peavy (12-5).