Crosby scored the tying run on Nathan's throwing error and Brown followed close behind with the game-winner as the Athletics rallied in the bottom of the ninth to beat the Twins 3-2 on Saturday night.
"I was hoping [Brown] was going," Crosby said. "I looked up and I knew the third baseman wasn't going to get it so right when I hit home I turned around hoping he was charging right behind me."
Nathan's first fielding error of the season cost Minnesota a win and a chance to move into first place in the AL Central. Front-running Chicago lost to Boston but the Twins couldn't take advantage and remained a half-game behind the White Sox.
Jack Cust homered and Huston Street (5-5) pitched two scoreless innings for the A's, who rallied for their 10th walkoff win of the season and second in three days. Kurt Suzuki hit a game-winning double in the ninth inning Thursday in a 3-2 win over the Twins.
Crosby singled off Nathan (0-1) leading off the ninth before the Minnesota right-hander hit Brown to put runners on first and second. Ryan Sweeney then attempted a sacrifice bunt, but Nathan fielded the ball and tried to throw to third. The ball skipped past Twins' third baseman Brendan Harris and into the spacious foul territory at McAfee Coliseum and Crosby raced home, with Brown scoring behind him.
"It wasn't a bad bunt and Bobby can run a little bit, too," Brown said. "It would have taken a perfect throw in a perfect spot to get him. I was kind of shocked by it."
Twins manager Ron Gardenhire wasn't surprised Nathan attempted the throw, citing the right-hander's otherwise flawless fielding this season.
"Joe's a very good athlete and a very good fielder," Gardenhire said. "He could have made that play. You miss one play in a game and it's a tough loss. It's not an easy throw."
Cust hit his 25th home run of the season in the fifth for Oakland, which had been held in check most of the night by Minnesota lefty Francisco Liriano.
Liriano allowed five hits over seven innings, struck out five and didn't walk a batter for the first time this season but was denied his fifth win in August when the Twins' bullpen failed to protect a 2-1 lead. Nathan had been successful on 36 of 40 save attempts before losing to Oakland.
A day after hammering out a season-high 20 hits in a 12-2 win over Oakland, the Twins managed only six singles and one extra base hit while losing for the sixth time in their last eight games.
Dallas Braden gave up two runs -- one earned -- and seven hits over six strong innings for the A's.
The Twins pressured Braden early and had runners in scoring position three of the first four innings before Span's home run in the fifth broke the scoreless tie. Span's homer, his fourth of the year, came two batters after Alexi Casilla reached on a fielding error by Oakland rookie third baseman Cliff Pennington.
Cust homered on the first pitch from Liriano in the bottom of the fifth to cut Minnesota's lead in half but Oakland managed only one hit the rest of the way until Crosby's leadoff single in the ninth.
It didn't help that the A's were without designated hitter Frank Thomas, who was placed on the 15-day disabled list because of a strained right quadriceps prior to the game. Thomas was in manager Bob Geren's original lineup and was on the field two hours before the game before being scratched after taking batting practice
It is the second time the 40-year-old power hitter has been on the DL this season. Thomas, who is tied with Willie McCovey and Ted Williams for 17th place with 521 career home runs, missed 55 games with tendinitis in his right quad from May 28-July 30.
After the game Geren acknowledged the injury may end Thomas' season.
"He is going to get further tests soon but that is a possibility," Geren said. "Being that's a similar feel and in the same spot, it's a possibility, yes."
The A's also reinstated RHP Keith Foulke from the DL, optioned LHP Dan Meyer to Double-A Midland, transferred RHP Andrew Brown to the 60-day DL and called up OF Aaron Cunningham from Triple-A Sacramento. ... Cust struck out in the seventh and leads the AL with 167. The Oakland single-season record of 175 was set by Jose Canseco in 1986. ... The Twins plan to add relievers Bobby Korecky, Phillip Humber and Jose Mijares and four other reinforcements from the minors for the stretch run.