With one out in the ninth, Murphy saw his chance -- a Neftali Feliz changeup left over the plate -- and drilled a game-tying, two-run blast to right to send the game into extras. Three innings later, Michael Brantley provided the finishing blow with a walk-off solo homer to seal the Tribe's 4-3 victory at Progressive Field.
The win completed Cleveland's first series sweep since it took three games in a row against Boston on June 2-4.
"There's something to be said for 'keep playing,'" Indians manager Terry Francona said. "There wasn't a lot to yell about during the game, but our pitching kept it close enough. Murphy hits it out of the ballpark and we got to keep playing."
Murphy, who signed with the Indians this offseason after playing in Texas for seven seasons, proved a thorn in the side of his former club all weekend. With his 2-for-3 performance on Sunday, the 32-year-old finished the series 6-for-10 with a homer and five RBIs, adding a handful of standout throws and diving catches to boot.
"You get pumped up to play your friends," Murphy said. "It probably helped a little bit that I faced some guys that I know how to approach. I know how they pitch. I've seen them pitch a decent amount over the years. You could say that's an advantage. In the end, both times we've played them this year, I've been feeling good at the plate."
Murphy improved to 16-for-38 over his last 12 games after hitting .136 over his previous 28 games.
On the same weekend that Jim Thome officially retired as a member of the Tribe, Brantley channeled some late-game heroics of his own, as well. In fact, the outfielder became the first Indians player to record two extra-inning walk-off homers in a season since Thome did so three times in 2001, according to ESPN. Brantley's other game-clinching long ball came in the 10th inning against Detroit on May 19.
Sunday's home run, hit off Texas reliever Phil Klein, gave Brantley a career-best 16 on the season.
"It's a 3-2 count, [Klein] can throw me anything with that count," Brantley said. "Just trying to put a good swing on a good pitch, and I was lucky enough to put a good swing and kind of lift it over the gate."
As he often does, right-hander Trevor Bauer overcame his early command issues and settled down down as the game wore on, ultimately holding Texas to three runs on six hits over a career-high 7 1/3 innings. The right-hander has posted a 3.86 ERA over his last six outings, five of which have been quality starts.
"It's just a matter of me getting comfortable," Bauer said. "Once I get comfortable and settle in, I can really up the intent. I've tried to throw as hard as I can from pitch one and I spray balls everywhere still. It's something I've been trying to address for six, seven, eight years. It's one of the ones I haven't been able to figure out yet."
Yu Darvish befuddled the Tribe over seven innings, allowing just four hits while recording eight strikeouts. Fittingly, Murphy produced the team's only run against the right-hander -- a two-out RBI double in the second inning -- before the offense was finally able to break through against the Texas bullpen.
Nick Swisher, who went 0-for-3 with three strikeouts, left the game after straining his right wrist while swinging at a breaking ball from Darvish. The team will examine the veteran on Monday in order to further evaluate his condition.
Six different Tribe relievers combined to keep the Rangers quiet over the final five frames -- four pitchers allowed just one batter to reach base during extra innings -- before Brantley ended the stalemate by going yard in the 12th. Scott Atchison picked up victories in consecutive games.
For Murphy, he was able to cap off the weekend in thrilling fashion and give his daughter the type of birthday present that you can't quite put a price on.
"It was fun to be able to do that on a day like that for her," Murphy said. "It makes it special."
Of course, succeeding against the team that let him walk as a free agent last winter surely made it a little sweeter.
"As much as you'd like to say it's just another game and that playing against another team that trades you or didn't bring you back, old teammates," Bauer said, "there's a little extra that goes into it. I'm just really happy for him."