"Our offense showed up late in the game. You just keep pounding the strike zone and eventually you're gonna score," Floyd said. "It's been a bit of a rough ride, but we're starting to come together as a team."
Only one of the three runs allowed by Floyd (1-2) was earned, but the White Sox again were giving the right-hander no offensive support -- they had scored only six runs his first four starts. It was 3-1 until the Rangers faltered in the seventh.
Texas starter Scott Feldman was pulled after an error and a walk against the first two batters in the seventh. Darren O'Day (0-1) gave up an RBI single to A.J. Pierzynski and a walk to load the bases before Dustin Nippert threw a wild pitch that allowed the White Sox to score the tying and go-ahead runs.
Floyd then finished with a perfect bottom of the seventh. He struck out five with no walks and ended a personal five-game road losing streak that dated back to last season.
"He was great. We needed an outing like that from him to build his confidence back," manager Ozzie Guillen said. "Now he's getting in a groove and throwing the ball better."
Konerko, who leads the majors with 10 homers, led off the eighth just clearing the 14-foot wall in left field to make it 5-3. His two-run blast in the ninth went to the back of the Rangers bullpen in right-center and proved to be the difference.
The only White Sox run early came on a sacrifice fly by Konerko.
"He's been carrying this ballclub," Guillen said. "Hopefully he'll continue to do that."
Texas scored twice in the bottom of the ninth off closer Bobby Jenks, making his first appearance since Sunday in non-save situation.
Feldman, a 17-game winner last season, had failed to get past the fourth inning in either of his last two starts. But the right-hander was facing the bottom part of the Chicago lineup to start the seventh.
Alex Rios reached when rookie first baseman Justin Smoak dropped a throw for an error, then Mark Kotsay walked. O'Day pitched for the first time in a week after back stiffness. After getting Juan Pierre on an infield popout that had Guillen dropping his head in frustration, O'Day loaded the bases with a walk to slumping Gordon Beckham.
Nippert then threw a curveball that bounced away from the plate. Kotsay scored from third and when catcher Max Ramirez made an errant throw wide of Nippert covering the plate, Pierzynski rounded third and came home to make it 4-3.
"When there are outs to made, you need to make outs," manager Ron Washington said. "The wild pitch is going to happen. But the thrown ball not being caught, that's what hurt us."
Nippert said it was a "bang-bang play" and that the ball clipped off the tip of his glove when he tried to make a quick sweeping tag.
Andruw Jones, at the plate when the wild pitch was thrown, was retired on an inning-ending groundout but the damage was done.
Beckham was in a 4-for-34 slide before a leadoff double in the fourth. He advanced on a grounder and scored on Konerko's deep flyball to right.
Josh Hamilton had three hits for the Rangers, who wrapped up a 4-3 homestand.
Smoak, the switch-hitter playing his seventh major league game, pulled a pitch into the second deck of seats in right field in the fourth for his first major league home run. The 402-foot blast put the Rangers up 3-1, and he added an RBI double in the ninth.
Texas went ahead with two unearned runs in the third after Julio Borbon tripled into the left-center field gap.
Joaquin Arias hit a grounder down the third base line that chased Borbon back to the bag. But Mark Teahen threw the ball wide of first base, allowing Borbon to score and Arias to go to second before Hamilton's RBI double.
RF Carlos Quentin was scratched from the White Sox starting lineup because of a sore left hamstring. Guillen said he probably won't play Friday, but should be fine by Saturday. ... It was Konerko's 25th career multihomer game. ... The wind was blowing at 27 mph with gusts to 40 mph. ... It was Washington's 58th birthday. ... 3B Michael Young is the only Rangers player to start every game this season after SS Elvis Andrus got his first day off. ... Young had one of the shortest groundouts possible. He had a check swing in the fifth, and the ball rolled just in front of the plate. Catcher Pierzynski picked it up and tagged Young, who hadn't even gotten out of the batter's box.