David Murphy followed Davis' home run with one of his own, and the Rangers have a half-game lead over the Angels going into a nine-game homestand that starts on Friday night.
"That was a big win," winning pitcher Eddie Guardado said. "It was a grinder tonight. It was a grinder the whole game, especially in extra innings. But it's a great win. Games like this build a tight group and builds chemistry because everybody is pulling for each other. That's what it was all about."
This was the longest game by time (four hours, 22 minutes) and innings for the Rangers this season. The Rangers are 4-3 in extra-inning affairs.
"It came down to the last team standing, and we won it," manager Ron Washington said. "We're still fighting to get back to where we were. We're not there yet, but we're still fighting. Tonight was a good feeling."
Davis' home run finished off a season-high four-hit night for him and was just his second home run in 24 games. He was hitting .169 with one home run, five RBIs and 34 strikeouts in 23 games since his two-homer night against the Yankees on May 26 until Thursday's breakout.
"It definitely feels good to swing the bat well like that, especially the whole game," Davis said. "This was a battle the whole game. They had no quit in them. This was a mental and physical battle. Both clubs fought well. I was glad we came away with the victory."
The Rangers, in a 6-6 game after 11 innings, needed both home runs because Jason Jennings gave up a two-run single to Miguel Montero with two outs in the bottom of the 12th. But he retired Ryan Roberts on a grounder to shortstop Omar Vizquel to earn his first career save.
"We kind of escaped here with a little momentum," Jennings said as the Rangers finished with two wins after four losses to start the road trip. "It was not a good trip but a good way to end it."
The Rangers led, 6-4, going into the bottom of the eighth inning, but Justin Upton reached on a one-out infield single and Mark Reynolds tied the game with a two-run home run off Francisco.
Francisco had been successful 17 straight save opportunities going back to Aug. 18, 2008. He had allowed just one run over his first 21 appearances and 21 2/3 innings this season. Washington said Reynolds' home run had nothing to do with Francisco pitching in back-to-back games for the first time since coming off the disabled list.
"A good fastball hitter caught a good fastball," Washington said. "He threw him a fastball, and he got it. I thought Frankie's velocity was good and the ball was coming out of his hand good. Frankie is only human. That Reynolds kid has good power."
Reynolds hit two home runs in the game. He also hit a two-run shot off Scott Feldman in the first inning. Feldman went six innings, allowing three runs on four hits and a walk and was in line to get the victory until Francisco let it slip away. Feldman is without a win in his last four starts.
"It's really nice to get out of here with a win regardless if there is a 'W' by my name or not," Feldman said. "A long plane ride home is better considering it was a battle, but we still pulled through."
Both teams had multiple chances to win long before the 12th inning. The Rangers finished with 15 hits and the D-backs' nine pitchers walked six. But the Rangers went 3-for-16 with runners in scoring position on the night before their power pulled them through in the end.
"We swung the bats like the Texas Rangers in that last inning," Washington said.
Nelson Cruz, snapping an 0-for-18 skid, started the winning rally with a one-out double off of reliever Esmerling Vasquez. That brought up Davis, who had already reached base four times on two singles, a double and a walk.
This time, he worked the count 2-2 and barely tipped a 94-mph fastball to stay alive. He then got a changeup and hit it over the right-field wall for his 14th home run of the season.
"He threw that first one by me, and I barely got it," Davis said. "I could hear his frustration on the mound. I stepped out and collected myself. Then he threw a changeup over the plate and I just threw my hands at it and hit it well."