Willits, one of the fastest players in the organization, had entered the wild game as a pinch-runner after Tigers closer Todd Jones threw away Kendry Morales' high hopper down the third-base line leading off the 10th inning.
After the single and error, Maicer Izturis was walked intentionally and Jose Morales executed a perfect bunt, another element of the Angels' game.
Up came Aybar, the rookie who'd ended two defeats earlier in the season getting thrown out trying to steal second.
Electing to face Aybar rather than Gary Matthews Jr., who'd delivered a pair of hits and scored twice, Tigers manager Jim Leyland watched the Angels beat his closer, Jones, without a ball leaving the infield -- little ball to the extreme.
The win went to Dustin Moseley (2-0) for getting the last out of the 10th in relief of Darren Oliver with two runners aboard.
Guerrero tied it in the ninth, when he went the other way against Jones with one out for a ground-rule double to right for his third hit of the day, raising his average to .403.
When Garret Anderson flied deep to center, Guerrero took flight for third with his long strides and got there. Alertly focused, the superstar right fielder bolted for home when Jones bounced a pitch to Casey Kotchman, beating Ivan Rodriguez's hurried toss to the pitcher after the ball bounded no more than 20 feet from the plate.
"He doesn't panic, that's the big thing," Angels starter Kelvim Escobar said of Guerrero. "That's the game, right there. Either he ties it, or he's out and the game's over. That was the key, right there, to coming back and winning."
Escobar, coming off the 15-day disabled list with shoulder irritation, lasted 5 2/3 innings, the Tigers patching together a three-run sixth that shaved the Angels' lead to 7-4.
"I felt strong the whole way," said Escobar. "It wasn't like I was all over the place with the ball. I was very close on so many pitches. They could have gone either way, but give their hitters credit for being patient."
The Angels had used their legs as well as their bats in forging a 7-0 lead after three innings.
Matthews singled against Jeremy Bonderman leading off the first, stole second and scored on Orlando Cabrera's double. Guerrero's single had runners at the corners when the first of two errors by shortstop Carlos Guillen, on Kotchman's grounder, made it 2-0.
Another run scored when Guillen couldn't handle Bonderman's feed on Morales' tapper, and Izturis' RBI single had Escobar -- unaccustomed to such support -- in front, 4-0.
Guerrero's two-run single on a searing line drive to right center made it 6-0 in the third, behind singles by Matthews and Cabrera.
The Tigers began chipping away with an unearned run, courtesy of two Angels errors, by Izturis and Aybar, in the fourth. After Justin Speier rescued Escobar in the sixth, Scott Shields saved Speier in the seventh, getting Gary Sheffield to hit into a double play after Curtis Granderson's second homer in two days had made it 7-5.
It was more of the same anxiety for the Angels in the eighth. Three walks -- Polanco's free pass forcing in a run -- cut the lead to 8-7 before Rodriguez retired Granderson to leave the bases loaded.
Sheffield smoked a double to left-center with one out in the ninth and stole third. That might have unnerved K-Rod, who blew his first save of the season when he served up a two-run blast to Ordonez, a fellow Venezuelan, seemingly completing a stunning comeback by Detroit.
But then came the ninth inning and Guerrero's theatrics, before Jones hastened his own demise by unwisely fielding Morales' chopper and setting in motion events ending with Willits' mad dash home.
"More times than not, our staff is going to hold leads," Matthews said. "It would've been great to do it in nine, but hey, what's one more inning?
"You'll hear guys say you never take anything for granted -- and you really don't. You obviously expected [leading 7-0] to get the win -- and we got it. Hey, find a way to get it done. This is a huge confidence builder for guys like Aybar to come through like that."