The Athletics tied a postseason record by starting four rookies — Parker, Donaldson, Yoenis Cespedes and Derek Norris.
Parker looked sharp early but allowed another run in the third because of a fielding mishap. With two out and a man on second, Berry chopped a soft grounder to the right side. Parker came off the mound to field it, but with the speedy Berry hustling to first, Parker lost control of the ball while scooping at it with his glove for an error that allowed Omar Infante to score.
"He wasn't trying to flip it, because he was closer to the bag than I was," first baseman Brandon Moss said. "He was just trying to grab it and it came out of his glove."
Avila's solo shot made it 3-1, and the A's couldn't take advantage of Verlander's rising pitch count.
"In the postseason you don't go out there and think about pitch count and keeping it low," Verlander said. "I'm just going to be aggressive, try to find the strike zone and throw quality strikes, and the pitch count will take care of itself."
Verlander led the majors in strikeouts for the second straight year, and Oakland was baseball's most strikeout-prone team. It showed toward the end of Verlander's outing.
After taking a called third strike for the third out of the sixth — Verlander's fourth strikeout in a five-hitter span — Donaldson chirped a bit at plate umpire Jim Reynolds. Verlander was done after one more inning, finishing with 121 pitches and his fourth career postseason win.
Verlander walked four.
"We battled him hard, but it doesn't even seem to matter how many pitches that guy throws," Oakland outfielder Josh Reddick said. "He just keeps coming after you with all of those pitches."
Benoit allowed a single in the eighth, followed by a flyout by Moss that Andy Dirks caught at the wall in right field.
"I didn't think it was gone," Tigers manager Jim Leyland said. "I thought he just missed it. And he did just miss it."
Oakland right-hander Pat Neshek, whose newborn son died 23 hours after his birth, came on to relieve Parker in the seventh. He entered with two on and one out but got out of the inning without any scoring.
Oakland wore patches with the initials GJN. Neshek's son's name was Gehrig John Neshek.
"It was really tough warming up, and I thought about him the entire time. I said yesterday that baseball would be a way to clear my mind, but that didn't happen. He was always there," Neshek said. "I know it is a cliche, but I really felt like I had someone watching me and helping with that last pitch. That was my best slider of the year."
NOTES: Parker allowed seven hits. He struck out five and walked one. ... Crisp was 8 for 22 off Verlander entering but with no homers. ... Cabrera received chants of "MVP" from the fans when he was announced before the game. Oakland 3B Brandon Inge — a former Tiger — was also cheered. ... Moss struck out three times. ... Arizona started four rookies three times in the 2007 postseason, according to STATS, LLC. ... Verlander also struck out 11 against the Yankees in last year's division series.