Konerko, who drove in four runs, took the big league lead in homers with his ninth, a solo blast leading off the eighth inning, and then retook the lead from Arizona's Kelly Johnson with another in the ninth. With that late blast, Konerko tied Jim Thome's White Sox mark for April home runs set in 2006.
"I'm certainly not trying to hit home runs. I have a good plan when I walk up there," said Konerko, who has a team-best 18 RBIs this season. "Just having an idea what I want to do and sticking to it. And if it doesn't work out, not panicking and just stay with my stuff and just trusting it.
"Not much else. Taking each at-bat as it comes with the situation in front of me and not trying to do anything. Just competing and that's it."
That's what manager Ozzie Guillen would like to see more of from all of his players, and he's been vocal about it, saying he doesn't want to see the team, which improved to 9-13, fall into a slump like the six-game road losing streak it busted out of Thursday.
Guillen isn't afraid to state the obvious: that if the White Sox fall too far behind in the American League Central, which they're expected to contend for every year by a demanding front office and fan base, major personnel changes could follow.
Then again, he's also not afraid to say that his club -- in its present state -- is quite capable of turning it around like it did Thursday.
"I'm not worried about it," Guillen said. "I'd be disappointed about the players because I truly believe with what we have out there, they should compete. If you look at this lineup, the pitching staff and relievers, I don't see why we're not competing.
"In the meantime, those guys are going to dictate to them what we should do for this year and the future. We don't play up to our potential. When you don't play to your potential, there are a lot of doubts in people's minds."
For six innings Thursday, those doubts were visible -- especially with the bats. The White Sox had two hits off Texas starter Scott Feldman prior to the seventh, with Gordon Beckham's leadoff double eventually turning into a run in the fourth.
The Sox produced only one hit in the seventh when rallying for three runs and a 4-3 lead. Alex Rios reached on an error when first baseman Justin Smoak couldn't scoop a low throw from shortstop Andres Blanco. Mark Kotsay walked on four pitches from Feldman, and A.J. Pierzynski greeted sidearm-throwing right-hander Darren O'Day (0-1) with a first-pitch single to right, scoring Rios.
Alexei Ramirez bunted both runners up one base, where they stayed at second and third when Juan Pierre popped out to second base. But a wild pitch from reliever Dustin Nippert with Beckham batting scored Kotsay with the tying run, and catcher Max Ramirez's throwing error trying to nail Kotsay allowed Pierzynski to score with the go-ahead run.
Gavin Floyd gave up three runs (1-2), including Smoak's first career home run with one out in the fourth. But two of the runs were unearned because of a Mark Teahen throwing error in the third.
Floyd kept the White Sox close enough to rally and won for the first time on the road since Aug. 15 at Oakland -- a span of seven starts.
"Today, our offense showed up a little bit later in the game and scored a lot of runs," said Floyd, who fanned five and didn't issue a walk. "That's your whole goal is to keep pounding the strike zone and try to get outs and eventually we'll score."
"Outstanding," said Guillen of Floyd. "The only reason I took him out is because I had my best lefty out there [in Matt Thornton] and he hadn't pitched in a few days. I was confident he would throw the ball good. We needed an outing like that from him. Start building his confidence back from the beginning of the season. I think he's starting to regroup and throw the ball better."
Texas rallied for two in the ninth off closer Bobby Jenks and had the winning run at the plate, before Joaquin Arias grounded out to Beckham, who made a nice barehand pickup and throw to end the game.
New York marks the next road stop in this early salvation project for the White Sox, a spot where the final hopes for 2009 playoff contention basically were dashed at the end of August, when the Yankees swept the White Sox by a combined 22-4 margin.
This time around, Guillen and the White Sox will try to take Thursday's momentum and use it to propel the team into a magnificent May.
"Believe me, it's a shame the way we're playing because I think this club is pretty good to compete," Guillen said. "And you look in the past of those guys and I think we should and we're not playing the way we should be playing."
"It has been a little bit of a rough ride," Floyd added. "But we are starting to put it together as a team."