Murphy's single off Rivera with the bases loaded in the 10th inning gave the AL West-leading Rangers a 4-3 victory Tuesday night in an early August matchup of division leaders with a playoff-type atmosphere.
After go-ahead homers in two Texas victories over the last week, Murphy hit another homer before his game-winning single off Rivera (3-2) and getting mobbed by his teammates after rounding first base.
"Sweet stroke, that's what we call him," Rangers starter C.J. Wilson said.
"I've been taking the single approach up there and looking out over the plate and reacting," Murphy said. "It's working right now and I'll stick with it."
It was Rivera's first loss in 32 career appearances at Rangers Ballpark, where he had been 2-0 with 17 saves while the Yankees had won 29 consecutive games there since August 1996 when he pitched.
Michael Young scored the winning run after leading off the 10th with an infield single, beating Derek Jeter's throw after the shortstop made a backhanded stop deep in the hole. Josh Hamilton followed Young with a rolling single through the right side of the infield.
Third baseman Alex Rodriguez, who hit career homer No. 601, made a run-saving defensive play with a diving stop of Vladimir Guerrero's grounder to throw him out while the runners advanced only a base. Nelson Cruz was intentionally walked to load the bases before Murphy hit a liner that dropped in right-center.
"No matter how hard they're hit, it's a hit," Rivera said. "In the newspaper, it will be a line drive. So it doesn't matter, they're hits."
Rivera's impressive streak against the Rangers included appearances in three consecutive playoff series New York won in the late 1990s that ended Texas' only postseason appearances.
New York (69-43) still has the best record in baseball and Texas has by far the largest lead in any of baseball's six divisions. The Rangers (65-47) are 8½ games ahead of the Los Angeles Angels.
Murphy's two-run homer in the sixth put the Rangers ahead 3-2 after he threw out a runner out at home plate, helped by a nice snag by catcher Bengie Molina.
Rookie closer Neftali Feliz (3-2), the fifth Texas reliever, pitched two scoreless innings in his first appearance since Thursday.
There was a crowd of 46,121 for a midweek game that began with a 98-degree temperature -- and on the same night the Dallas Cowboys drew more than 21,000 fans for a free public practice at their stadium across the street.
Rodriguez led off the eighth with his 18th homer this season, his 97th homer at Rangers Ballpark, his home for three seasons before getting traded to the Yankees before spring training in 2004.
Nick Swisher had a two-out RBI double to tie the game 1-all in the fifth, but was thrown out by several steps trying to score on Marcus Thames' hit when Molina snagged the short-hopped throw from Murphy in left field.
Molina made the nifty catch, dropped to his knees and casually tagged an obviously surprised Swisher, who rolled to the ground after trying to get around and then got up smiling.
"Two outs, you've got to send him," Yankees manager Joe Girardi said. "It was a great play by Bengie Molina to hold the ball."
That wasn't the only defensive gem for the Rangers on a night when they tied a season-high with three errors.
Wilson fielded Jeter's high chopper on the run in the third inning and dived headfirst into first base to tag the bag with his glove just before Jeter got there. Jeter tumbled over the pitcher without stomping on him.
Wilson left with two on and one in the sixth after 96 pitches, and reliever Darren O'Day gave up an RBI single to Francisco Cervelli that put the Yankees up 2-1.
Yankees starter A.J. Burnett struck out four and allowed three runs over seven innings.
Notes: Despite giving up the RBI single to the only batter he faced, O'Day was credited with his team-record 27th consecutive scoreless appearance. Jeff Zimmerman had 26 straight in 1999. ... Yankees 1B Mark Teixeira was not in the lineup and won't even be in Texas for the two-game set. He remained home after the birth of his third child earlier Tuesday. ... A fan sitting in the first row near the Yankees dugout was hit by parts of Jeter's shattered bat in the seventh. He was tended to by medical personnel for what appeared to be a slight cut on his head, then put his cap back on and stayed for the rest of the game.