New York trailed 4-1 at the end of the fifth inning but a seven-run sixth inspired the Yankees and ended their three-game skid.
Brett Gardner stepped up with four hits as the Yankees held on to beat the Rangers.
Mark Teixeira also chipped in with his 18th homer, while walking three times and scoring as many runs.
The Yankees (55-51) remain 4.5 games adrift of the American League East division-leading Baltimore Orioles (59-46), who claimed back-to-back wins with a narrow 7-6 victory over the Los Angeles Angels.
Toronto (58-50) are within touching distance of the Orioles after they downed the Boston Red Sox 4-2 - the Blue Jays' fourth consecutive victory.
The Blue Jays - led by Colby Rasmus' solo homer and Anthony Gose's tie-breaking two-run double - are 2.5 games behind Baltimore in the AL East.
In other results on Tuesday, the AL Central-leading Detroit Tigers slumped to a fourth successive defeat following their 11-4 loss to the Chicago White Sox.
National League Central division pacesetters the Milwaukee Brewers were beaten 5-1 by Tampa Bay Rays.
The Cincinnati Reds shutout the Arizona Diamondbacks for a 3-0 win and the Miami Marlins - on a six-game winning streak - downed NL East rivals the Washington Nationals by the same scoreline.
Cole Hamels pitched eight scoreless innings as the Philadelphia Phillies disposed of the New York Mets 6-0.
The Minnesota Twins defeated the Kansas City Royals 2-1 and the Seattle Mariners overcame the Cleveland Indians 5-2.
The Houston Astros lost 7-4 to the Oakland Athletics, while the Pittsburgh Pirates were 3-1 winners over the San Francisco Giants 3-1.
The Los Angeles Dodgers beat the Atlanta Braves 8-4, the St Louis Cardinals suffered a 3-1 loss to the San Diego Padres and the Chicago Cubs edged the Colorado Rockies 4-3 after 16 innings.