The A's joined Atlanta as the only teams to win 11 division titles.
With the victory, the Athletics avoided a trip to Tampa Bay for a makeup game Monday and got extra time to prepare for the playoffs. Oakland's game at Tampa Bay on Sept. 18 was postponed because of Hurricane Gordon.
The Cleveland Indians beat Toronto 11-4 earlier in the day, preventing the A's from clinching a playoff spot prior to their game.
There had been talk that manager Art Howe would hold Hudson (20-6) if Cleveland lost, but the manager decided Saturday night he would start his ace no matter what.
"During the postseason, you want to have home-field advantage as much as possible. That's why I wanted Hudson to pitch," Howe said Sunday. "I wanted him to win here in front of the hometown fans, to get his 20th."
Hudson gave up four hits in eight scoreless innings and struck out 10. He became Oakland's first 20-game winner since Dave Stewart and Bob Welch each did it in 1990.
Hudsohas won seven straight starts. His last loss was Aug. 23 at Cleveland.
Jason Isringhausen pitched a scoreless ninth, working around two hits, for his 33rd save.
A day after the A's pounded the Rangers 23-2, the two teams were scoreless through six innings.
With two outs in the bottom of the seventh, Jeremy Giambi doubled and the sellout crowd started to buzz. Then Hernandez doubled off Ryan Glynn (6-6).
Velarde hit his home run to deep center field, his 12th of the season, in the eighth inning. An out later, pinch-hitter Saenz also homered.
Glynn, who finishes the season with a four-game losing streak, went seven innings, allowing two runs on two hits. He struck out four and walked four.
Texas had threatened in the fifth when Mike Lamb hit a single up the middle and Scott Shelton was hit in the shoulder with a pitch thrown so hard it knocked him over.
Randy Knorr's sacrifice bunt advanced Lamb and Shelton, but Scarborough Green's grounder was deftly handled by A's second baseman Velarde and Lamb was thrown out at home. Royce Clayton grounded out to end the inning.
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