Hinske hit a pinch-hit, two-run homer in the seventh inning and the Braves improved their wild card chances with a 3-2 win over the Florida Marlins on Tuesday night.
Hudson allowed seven hits, one run, walked four and struck out four in six innings.
"Hudson was outstanding. He had one of the best sinkers and moving fastballs I've seen from him all year," said Atlanta manager Bobby Cox, who started the right-hander on three days' rest.
As for Hinske, Cox said he knew his veteran left-handed hitter "was 0-for-10 against [Anibal Sanchez], but he got a pitch and he hit it."
Trailing 1-0, the Braves rallied for three runs in the seventh off Sanchez (12-12), who had held Atlanta to three hits in six innings.
Melky Cabrera led off the seventh with a single and was sacrificed to second. Brooks Conrad tripled off the center field fence, scoring Cabrera. On the play, Florida center fielder Cameron Maybin was injured when he hit the fence attempting the catch. He hurt his lower back and was taken off the field in a golf cart.
"I thought it was his leg, but it was his lower back. We'll see how it is in 2-3 days," Marlins manager Edwin Rodriguez said.
After Rick Ankiel struck out, Hinske hit a 2-2 pitch well over the right-center field fence for his 11th home run and a 3-1 Atlanta lead.
"I hadn't done much against him. I knew he had struck me out three times but I had hit some balls good off him," Hinske said of Sanchez.
"I was mad that I didn't swing at the first pitch he threw me, a change, that was up a little. I then got a fastball out over the plate," he said of the home run pitch.
"It was a good pitch. He probably was waiting for it," Sanchez said.
"Hopefully, it's contagious. It's do or die time. We've got to win every game now," Hinske added.
"It didn't feel too different," Hudson said of the short rest. "I've done it before. It didn't bother me. I would have been sick if we had lost 1-0 giving up a couple of dribblers. Luckily, Eric got the big homer."
It was the seventh time Hudson had gone on three days' rest and was 2-0 with a 2.61 ERA in three regular season starts and 0-1 with a 3.97 ERA in three postseason starts. His last regular season start on short rest was Sept. 17, 2006, against the Marlins, allowing three hits and one run in seven innings.
Hudson was 1-4 with a 6.10 ERA in five previous September starts after going 6-0 with a 1.43 ERA in his previous eight starts.
The Braves improved their home record to 54-23, tops in the majors.
The Braves have four games left -- all at home -- against Florida on Wednesday and three games with NL East winner Philadelphia beginning Friday night. ... Atlanta LHP Eric O'Flaherty who last pitched on Wednesday, is not available. He said he has been suffering from lightheadedness, dizzy spells and blurred vision and is undergoing tests. It could be related to a spell of mononucleosis, which had him on the DL from July 10-Aug. 20. ... Braves 3B Martin Prado will be out for the season after an MRI on Tuesday showed he had a hip pointer and a torn exterior oblique muscle after he injured himself while swinging at a pitch in Monday night's 2-1, 11-inning win over Florida. The Braves will start Derek Lowe on three days' rest on Wednesday. ... Florida SS Hanley Ramirez did not start for the seventh straight game because of a sore left elbow and right elbow.