Floyd allowed four hits over 7 2/3 innings and Quentin hit a three-run homer in the fifth to give the White Sox a key 3-0 division victory over the Cleveland Indians on Friday night.
"These are formidable opponents and we're looking to play well against them," Quentin said after the White Sox opened a stretch of six straight games against Cleveland and Detroit -- the two teams ahead of them in the standings.
Floyd (8-9) earned his second straight win after going 0-4 over six previous starts. The right-hander struck out five and didn't issue a walk for the first time in 19 starts.
"I will enjoy it tonight, but then it is back to work tomorrow," Floyd said. "We have a lot of big games coming up."
Floyd got help from a resurgent Chicago bullpen. Sergio Santos, the second reliever used by manager Ozzie Guillen, struck out Matt LaPorta on a pitch in the dirt with a runner on second in the ninth for his 19th save in 22 chances.
Matt Thornton replaced Floyd with runners on second and third in the eighth. Pinch hitter Orlando Cabrera drove his first pitch toward the gap in left-center, but left fielder Juan Pierre made a running catch near the warning track to end Cleveland's best scoring threat.
"The pitching staff did the job and Carlos got a big hit," said Guillen, sporting a bruise under his right eye where he was hit by a foul ball in the dugout Wednesday during an extra-inning loss in Kansas City.
"We play the teams we're chasing," he said. "It's very important to stay close to them. If we get too far behind, we're creating a dangerous situation for us."
Chicago improved to 12-20 against AL Central opponents by winning for just the sixth time in its past 15 games overall. The second-place Indians have lost five of seven and are 3 1/2 games ahead of the White Sox.
"There's not much you can do when you can't score any runs," Indians manager Manny Acta said.
Quentin's 20th homer came off Carlos Carrasco (8-8), who worked out of several early jams. The right-hander stranded two runners in both the first and second innings and left the bases loaded in the third.
"Carlos gave us a chance, despite having to battle all that traffic," Acta said. "Unfortunately, he couldn't work himself out of all of them."
"It's hard to string together three hits in a row against him," Dunn said. "He can be really, really tough."
Quentin is a key reason why the White Sox are 5-1 this year against Cleveland. He is batting .500 (11-for-22) with three homers and 12 RBIs in the season series.
"I got a pitch middle in and put some wood on it," Quentin said of his homer. "Gavin is the story. He was unbelievable."
Floyd retired the first nine Indians. Ezequiel Carrera singled to open the fourth, but was erased on a nifty double play. First baseman Konerko scooped up a sharply hit ball by Brantley at his ankles and threw to shortstop Alexei Ramirez to force Carrera. Ramirez then sidestepped the sliding runner, jumped up and threw to first, where Floyd dug out the low throw.
That was the type of play Guillen wants. After the tough loss Wednesday, he questioned his team's focus.
"I made the comments that when we go to Cleveland and play Detroit, Boston and New York, we have to be better," he said before the game. "I don't think I was lying or making stuff up.
"My job is to win games, but we're not winning games. Was I frustrated? Yes, but it's not just me. We all should be. I know this ballclub better than anyone and we know we have a better ballclub than we've shown."
"We've been in this situation before," Guillen said. "As long as I'm here, I'm going to push as hard as I can."
Carrasco gave up six hits and three runs over 6 1/3 innings, striking out six. After going 4-2 with a 1.90 ERA in June, the right-hander is 0-4 with a 7.40 ERA in four July starts.
Rain delayed the start 47 minutes. ... Cleveland called up 2B Jason Kipnis from Triple-A Columbus and he went 0-for-2 and was hit on the knee by a pitch in his major league debut. Kipnis was the Indians' second-round draft pick in 2009. ... The Indians optioned INF Luis Valbuena to Columbus and designated for assignment minor league INF Jared Goedert to clear roster room for Kipnis. ... Pierre went 0-for-4 with a walk, ending his 12-game hitting streak. ... Dunn went 2-for-5 with one strikeout. He was 7-for-79 (.089) with 40 strikeouts in his previous 22 games. ... Hafner played his 1,000th career game.