Minnesota bounced back from Monday night's 20-6 rout by the Rangers when Texas scored the most runs in the majors this season.
The Twins trailed 8-7 when they put runners on second and third off Feliz (0-2) on Delmon Young's single and Jim Thome's pinch double.
Mauer, getting a game off on a 101-degree night, lashed a double to left to score pinch runner Jason Repko and put the Twins in front.
Nathan allowed two baserunners with one out, but recovered to strike out Mitch Moreland and pinch hitter David Murphy to record his 254th save with the Twins, tying him with Rick Aguilera for the club record.
Yorvit Torrealba homered and went 3 for 4 with four RBIs for Texas.
Nelson Cruz maintained his hot streak for the Rangers by going 3 for 3 with two RBIs. Cruz is 15 for 25 with 12 RBIs over his last six games to raise his average from .239 to .267.
Torrealba, who started the night in a 1 for 16 slide, hit a three-run blast in a five-run fourth, going deep for the first time since April 25.
The Rangers had won 16 of their last 19.
Texas countered with a two-run second on consecutive RBI doubles by Cruz and Mitch Moreland.
In the fourth, Cruz's second double of the game drove in Michael Young from first to tie it at 3.
Torrealba deposited Carl Pavano's 1-0 pitch into the left field seats for his fourth homer of the season, and Andrus' RBI single later in the fourth made it 7-3.
The Twins rallied with a three-run fifth as Wilson walked the first three batters of the inning, then gave up a two-run single to Danny Valencia that knocked Wilson from the game. Valencia stretched his career-best hitting streak to 10 games.
Each runner advanced a base on left fielder Josh Hamilton's throwing error, and Nishioka's infield single off Hunter drove in Valencia from third to pull the Twins within 7-6.
Torrealba's RBI single in the fifth stretched Texas' advantage to 8-6, but Jason Kubel's run-scoring single in the sixth got the Twins within one.
Wilson allowed six runs and seven hits with three strikeouts and four walks over four innings in his shortest outing of the season.
Pavano gave up a season-high eight runs with nine hits in five innings.
Notes: Feliz had his fifth blown save of the season. ... Minor league OF Leonys Martin, the Cuban defector who signed a $15 million contract with the Rangers this season, is spending two days with the big-league club working with coach Gary Pettis on baserunning and outfield play. Martin will return to Triple-A Round Rock after the two-day tutorial, where he'll probably finish the season. ... Twins 1B Justin Morneau experienced migrain headaches during a rehab workout in Minnesota on Tuesday and shut the session down. Manager Ron Gardenhire said Morneau felt better after taking medication and could resume workouts on Wednesday. Gardenhire said he'd been told by team medical personnel that the headaches were not related to Morneau's past neck and concussion issues. Morneau is on the 15-day DL with a sprained left wrist.