"They know I've been through a tough time early on this year, they know I'm here for everybody, that I just want to contribute," the 35-year-old designated hitter said Friday night after lining a leadoff homer in the bottom of the ninth inning to give the AL East leaders a 2-1 victory over the Chicago White Sox.
"Before I went up there, everyone's telling me to end the game, so I had a little more pressure than I wanted to have. To just contribute to this team, the way we've been winning, it makes you sleep a ton better."
Floyd's fourth homer of the season -- second since coming off the 15-day disabled list following knee surgery -- came against Scott Linebrink (2-1). It also ended a stretch in which the White Sox bullpen had not allowed an earned run in 28 innings.
"Linebrink brings the fastball," Floyd said, "If you go up there looking for anything else, you set yourself up for failure."
Said Linebrink: "I made my pitch. He went down and got it."
A crowd of 14,679 saw the Rays win a matchup of division leaders and raise their league-best record to 33-22.
Floyd homered on an 0-1 pitch and enabled Tampa Bay to overcome going only 1-for-8 with runners in scoring position. The AL Central-leading White Sox were even worse in clutch situations, finishing 1-for-9 with eight of the at-bats coming in the first four innings.
"This type of game happens when your offense don't do what it's supposed to do over the course of nine innings," White Sox manager Ozzie Guillen said.
"The bullpen has been great. We win a lot of games by one run, late in the game. It was a great baseball game. Too bad it ended like that."
Dan Wheeler (1-3), the fourth Rays pitcher of the night, worked one scoreless inning for the victory.
Contreras limited the Rays to one run and five hits in seven innings. Matt Thornton worked the eighth and Linebrink entered in the ninth.
The Rays took a 1-0 lead on B.J. Upton's RBI single in the third inning.
Alexei Ramirez homered in the fifth for the White Sox. Shields allowed one run and seven hits in six innings.
Both starters were coming off eight-inning outings in which neither was involved in the decision. Contreras gave up two runs and three hits in a game Chicago eventually won against the Los Angeles Angels, while Shields allowed four runs and eight hits before the Rays scored in the ninth to beat Baltimore last Sunday.
The White Sox squandered scoring opportunities in the second, third and fourth innings before breaking through against Shields on Ramirez's second career homer.
The Rays bailed their starter out of two jams with double plays, and Chicago wasted a leadoff double by Jermaine Dye in the fourth.
"We need the offense to pick it up and help the pitching staff," Guillen said. "We had a lot of chances, and we didn't make it happen."
The home run was the fifth Shields has allowed in his last three starts. He yielded two in his first nine outings.
White Sox SS Orlando Cabrera singled in the third inning for his 1,500th career hit. A.J. Pierzynski got his 1,000th in the fifth on a pop fly that fell between three Rays in shallow center. He was thrown out trying to turn it into a double. ... Chicago INF Juan Uribe (strained right hamstring) is expected to reinstated from the 15-day disabled list and rejoin the team for Saturday's game. ... With INF Ben Zobrist optioned to Triple-A Durham, the Rays plan to use rookie 3B Evan Longoria as their backup shortstop. Longoria played the position for about 20 games in college at Long Beach State, however manager Joe Maddon stressed he is the team's third baseman.