The victory was his first against the Twins since July 11, 2009. The slump marked the longest losing streak by a starting pitcher against one team since Jamey Wright lost nine in a row against Houston between 2000 and 2005.
"Curveball, slider, fastball," Floyd said. "I just felt like I had pretty good command on both sides of the plate with pretty much everything."
Rios broke a scoreless duel in the fourth with a two-run homer off Twins starter Liam Hendriks (0-5). Paul Konerko registered a one-out walk before Rios' shot to the second deck in left field, his ninth home run.
Rios also scored an insurance run in the seventh, coming around on a single from Alexei Ramirez. Rios opened the inning with an infield single and advanced to second on a steal before Ramirez's bloop hit to right. Ramirez is hitting .382 over his last 16 games (21-for-55).
The output felt like a lot more than just three after being held to one run or less in four of their last six games.
"Any time you can score a run, it's a big thing," Rios said of his homer. "Lately, we haven't been scoring so many runs. It's good to put the team on the board and the way Gavin pitched, that's all we needed."
Floyd controlled Minnesota's hitters for most of the night after allowing a leadoff double to Denard Span in the first inning.
"Everything was working for him," Ben Revere said of Floyd's performance. "His curveball, his slider and he was going inside and outside with his fastball and his changeup. If you do that -- and with the home run by Rios -- it's tough to score runs against him."
Floyd also escaped jams in the second and seventh innings.
He hit Ryan Doumit with two outs in the second, and then allowed a single to Alexi Casilla. Both runners advanced on a wild pitch, but Floyd covered first to finish the ending with a 3-1 groundout from Jamey Carroll.
Joe Mauer and Josh Willingham tagged back-to-back one-out singles in the sixth, but Floyd then induced a strikeout and a flyout from Justin Morneau and Trevor Plouffe, respectively.
Before allowing no runs Tuesday and in 6 1/3 innings in his last start against the Cubs, Floyd had given up 35 earned runs in his previous six outings.
"A guy that has his stuff, it's [about] spotting it better," White Sox manager Robin Ventura said. "I think just having better command and not getting balls in the middle of the plate. Tonight he was able to stay away from the middle of the plate and work his way out of innings."
Matt Thornton pitched a clean eighth, but closer Addison Reed's appearance in the ninth included some drama.
Reed sandwiched strikeouts of Willingham and Plouffe around a walk to Morneau. Doumit doubled to left and Chris Parmelee was hit by a pitch to load the bases. Carroll's single drove in Minnesota's two runs before Reed ended the rally by getting Span to ground out to second.
"This is the way we play," Ventura said. "It seems like we have a lot of close games. Tonight, you're able to wiggle out of it."
An umpire's review confirmed a foul call on Span's deep drive down the right-field line in the third.
Third baseman Kevin Youkilis went 1-for-4 for the second straight night with the White Sox.