Damon's blast into the second deck in right field off Twins reliever Jesse Crain (2-2) continued a string of late magic for the Yankees (20-17), who have won a season-high five straight to improve to three games over .500. The last time the Yankees had three consecutive walk-off wins was Aug. 27-29, 1972.
"Johnny has done a lot of this for us this year, big hits late in the game," Yankees manager Joe Girardi said. "This is just another one."
As in the first two walk-off wins, where the final blows were delivered by Melky Cabrera and Alex Rodriguez, Sunday's game presented a variety of contributors to help the Yankees emerge on top.
"This team doesn't give up," Yankees captain Derek Jeter said. "Once you do something, you feel like you can do it again. We don't want to keep falling behind, but we've done it before. Every game, we've been pretty good about playing nine innings."
Burnett blanked the Twins through six innings, but he was matched inning-for-inning by a very impressive Kevin Slowey. Minnesota got to Burnett for two runs in the seventh, and A-Rod answered in the home half with a line-drive home run to left.
It was Rodriguez's third homer since returning from the disabled list and his second in as many days against Minnesota pitching, having belted the game-winner in the 11th inning Saturday. Cabrera brought in Hideki Matsui with a sacrifice fly later in the inning to take Burnett off the hook.
"I'm just getting my at-bats right now, just trying to get a good pitch to hit and put a good swing on it," Rodriguez said. "They've been pitching me very tough this series."
A sterling defensive play by first baseman Mark Teixeira may have saved the Yankees, though it was at least matched by an exceptional effort from Twins catcher Joe Mauer in the ninth inning, sending the game past regulation.
"Big people made big plays today to keep this game close," Girardi said.
In the eighth, Brett Tomko inherited a bases-loaded one-out situation from Jonathan Albaladejo and went to work against Denard Span, who hit a sharp ground ball to the right side. Teixeira dove to his right, stabbing the ball, and threw home to catcher Kevin Cash for a force out.
"I just dove and knew I had to throw home, because the way the game was going, one run was probably going to win it there," Teixeira said. "I was trying to knock it down and throw it home."
Said Tomko, who recorded the next out to escape unscathed and leave the bases loaded: "I saw him dive, and for a brief second, I [thought], 'I hope he catches it.' Then I saw him get up and start throwing it at me, and I forgot he was going to throw it home. I just tried to dive out of the way and just let him make the play."
As outstanding as Teixeira's snag and throw was, Mauer opened eyes with his athletic effort on a ninth-inning play, saving the winning run from scoring. With pinch-runner Brett Gardner at second base and one out, Francisco Cervelli hit a grounder up the middle that hit pitcher Jose Mijares' glove, bouncing back to the plate.
Mauer bolted from behind the plate and secured the ball, faking a throw to first as Gardner spotted home plate unguarded, breaking on instinct. Mauer then beat Gardner back with the tag, as Gardner slid headfirst and painfully rolled on Cervelli's bat.
"He's pretty quick," Gardner said. "Even when I came around third and he faked to first, when he broke home, I thought I still had a chance to beat him. It really wasn't even that close. He beat me probably by a full step."
Alfredo Aceves (2-0) hurled a scoreless 10th inning to record his second victory in two games, logging the win when Damon belted his team-leading 10th homer.
"Sometimes you wish we would make it a little more comfortable and win by five or six, but we're battling," Teixeira said. "That's a very good team across the way, and it seems like the Twins always play close games. If you win three in a row, it doesn't happen very much like that."
Burnett did not have his sharpest performance, walking six, but he held the Twins (18-20) scoreless until Matt Tolbert's run-scoring single in the seventh, snapping Minnesota's 0-for-21 skid with runners in scoring position. Another run scored when Burnett fired consecutive wild pitches.
The right-hander allowed two runs on six hits over 6 2/3 innings, striking out seven in a 123-pitch outing -- the most by a Yankee since Randy Johnson threw 129 on July 19, 2006.
"Between Tex's play and Gardy trying to score, everybody seems like they're just coming together more a little bit every day," Burnett said.
And Damon regained possession -- for a day -- of the replica World Wrestling Entertainment belt that the Yankees have passed around for a month, a gift to Damon from Burnett's children in April.
"It doesn't seem like we've had an easy game yet this year, but we'll take any victory we can," Damon said. "This is especially nice since we're able to win a series against the Twins. Hopefully we can close it out tomorrow."