After Texas scored four times to go ahead in the eighth inning Wednesday night, Chacon got three outs facing two batters -- stabbing a line drive to start an inning-ending double play -- and the Yankees went on to win 8-7 on Jason Giambi's two-run homer in the ninth.
"He kept us in position to do what we did," manager Joe Torre said of Chacon (5-3), who made his fourth relief appearance.
The first six batters in the eighth reached for Texas, which went ahead 7-6 after Michael Young hit a two-run single and scored on Hank Blalock's single. With the bases loaded and no outs, Chacon came on as the third pitcher in the inning.
"I was dancing around looking for a base to throw to. It happened to work out for us," Chacon said. "I stuck my glove out, it was there, and my feet did the rest."
Derek Jeter led off the ninth with a single up the middle against closer Akinori Otsuka (2-4) and Giambi followed with his 29th homer. It was Giambi's first homer in nine games and came after a 6-for-36 slump.
"If Jason was saving up for a hit, that was it," Torre said.
"Derek and I were talking in the on-deck circle. I told him to get me an opportunity," Giambi said. "I haven't been swinging the bat well but this makes up for it. My legs are beat up, my knee is sore, but you have to find a way to contribute."
New York (59-40) completed a six-game season sweep at Texas and got within 1½ games of first-place Boston in the AL East. The Red Sox lost 5-1 at Oakland earlier Wednesday. The Yankees also moved a half-game ahead of Minnesota and the Chicago White Sox in the wild card chase.
It was the first time since 1992 that Texas was swept at home in a season series of at least six games. That had never happened at Ameriquest Field, which opened in 1994 and where the Rangers played their 999th game Wednesday.
When Kyle Farnsworth's back stiffened up while warming up, the Yankees went with T.J. Beam to start the eighth, and the rookie gave up two hits before giving way to Scott Proctor, who Torre had said before the game wasn't available after pitching the previous two games.
Proctor couldn't get an out and Chacon, 4-3 with a 6.58 ERA in 11 starts before being demoted to the bullpen earlier this month, was brought in.
"I always have confidence in myself, but today was good, definitely a boost," Chacon said.
Mariano Rivera worked the ninth for his 25th save in 27 chances.
Alex Rodriguez hit his 22nd homer to start the four-run eighth that put the Yankees up 6-4.
Rodriguez hit a full-count pitch from Francisco Cordero onto the hill in center field -- a 417-foot shot. Bernie Williams then walked and Andy Phillips, whose two-run single in the first snapped an 0-for-18 slump, had another hit before Melky Cabrera's two-run double made it 5-4.
Cabrera advanced on a sacrifice bunt by newly acquired catcher Sal Fasano -- the first out -- before scoring on a wild pitch.
It was the ninth blown save of the season for Cordero, who lost his job as the Rangers closer after setting a major league record with five blown saves in April. Otsuka has converted 22 of 24 save chances before Wednesday night.
"I'm proud of the way our guys battled back. We just couldn't get the last three outs," manager Buck Showalter said.
Mench drove in three runs with a milestone two-run double for Texas and a sacrifice fly. Mark Teixeira and Blalock both had three hits.
Mench's two-run double in the second tied the game and was the 50,000th hit in the Rangers' 35-season history. That was set up after Teixeira had a leadoff walk and Blalock singled off Yankees starter Jaret Wright.
After Teixeira started the fourth with a single, Blalock drove him home with a double and went to third on a passed ball before the sacrifice fly by Mench.
Yankees center fielder Johnny Damon, who missed the first two games of the series with a stiff back, led off against John Rheinecker with a single, but was thrown out trying to score on Rodriguez's grounder to third. Williams loaded the bases with a two-out single before Phillips' two-run single.
- The Rangers have a day off Thursday, their first after playing 14 straight games since the All-Star break. They then play 17 days in a row, including a 10-day road trip.
- The Yankees had four hits in the first inning, matching their total in a 7-4 victory Tuesday night.