Fiers pitched six effective innings, Matt Olson and Khris Davis hit consecutive homers, and the Athletics beat the Tampa Bay Rays 4-3 on Tuesday night.
Oakland, at 34-34, is three games behind Texas for the second AL wild card.
"Obviously the record right now doesn't show how good we really are," Fiers said. "It's a long season. You can't look too far ahead or how far ahead some of the teams are ahead of us. We've got to come play every day and just battle every day."
Fiers (6-3) allowed two runs and three hits, and is 4-0 in seven starts beginning with his no-hitter against Cincinnati on May 7.
Liam Hendriks, Lou Trivino and Blake Treinen, who gave up Willy Adames' RBI single in the ninth en route to his 15th save, combined to strike out six and complete the four-hitter.
"We really haven't hit our stride yet," Oakland manager Bob Melvin said. "It's been a little of a fight and battle for us to this point but I think at some point we'll get past it."
Tommy Pham homered for the Rays, who are 16 games over .500 despite an 18-15 record at home.
"Kind of quiet at the plate," Tampa Bay manager Kevin Cash said. "We didn't do many things wrong, we were just pitched really, really tough."
The Rays are tied for first in the AL East with the New York Yankees, who split a day-night doubleheader with the Mets.
After Matt Chapman reached on shortstop Adames' throwing error in the sixth, Olson hit a two-run homer and Davis then went deep two pitches later off Emilio Pagan (1-1) as Oakland took a 4-2 lead.
Pagan, acquired by Tampa Bay from the Athletics in a three-team trade in December, had allowed just one run over 19 innings in his previous 18 appearances.
"No one likes doing bad," Pagan said. "Doesn't make me any more upset than it would anybody else."
Pham put the Rays up 1-0 on a first-inning homer. He had been 1 for 17 in five games since returning June 6 from lower right leg injury.
Adames walked with two outs in the fourth, went to third on Kevin Kiermaier's single and scored to make it 2-0 on a double steal.
Oakland got to 2-1 on Chad Pinder's RBI single in the fifth.
Athletics: SS Marcus Semien played in his 150th consecutive game, dating to last June 28. "He's as durable a player as I've ever had, so at this point in time I don't see a day off for him," Melvin said. Semien extended his hitting streak to nine games (16 for 39) after leading off the game with a double.
Rays: DH Austin Meadows finished his at-bat in the eighth after fouling a ball off his lower right leg. Soreness in the leg will likely keep him out of Wednesday's lineup. ... INF Joey Wendle (fractured right wrist) could be back Thursday.
Oakland RHP Tanner Anderson, who allowed two runs over 5 2/3 innings in his first major league start Monday, will get another start. "He was impressive," Melvin said.
IN THE FOLD
The Rays signed SS Greg Jones, who was taken 22nd overall in this year's draft. He hit .341 and stole 42 stolen bases for UNC Wilmington.
Melvin presented long-time director of team travel Mickey Morabito with a birthday cake that featured a plane with stairs stuck in the wing. Morabito arranged for a new plane Sunday when the original team charter was damaged during a storm while Oakland was playing at Texas.
Oakland LHP Brett Anderson (6-4) will face Rays RHP Yonny Chirinos (7-2) opener in Wednesday's series finale.
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