Tyler Flowers and Konerko also homered for the White Sox, who won their fourth straight overall.
The White Sox were 5-13 against the Tigers in 2011, including the last six meetings.
"You want to win divisional games. Tigers are going to be there, they're too good of a team, they're going to be there, all we can hope is that we're going to be in the mix at the end and be in that fight, too," Konerko said. "All I know for sure is that those two games are in the books. Other than that I don't know anything else so it is good to get those two games and put them in the books."
The White Sox improved to 4-0 in the division.
Floyd (1-1) pitched around three walks and three hit batters. He struck out six and allowed only three hits.
"I thought he did a good job of taking advantage of our aggressiveness," Tigers manager Jim Leyland said. "He got a lot of swings on balls, on bad pitches. It was a pretty good game plan on their part. We're an aggressive team and he took advantage of that."
"I just got hit in the shoulder, and it's my throwing arm. Just to be safe, you might as well come out of the game and not risk anything," said Wilk.
Wilk (0-1) left with a bruised shoulder but is expected to make his next start. He allowed two runs on three hits in five innings Saturday. He struck out four and walked one.
"I thought he did a good job. He moved the ball around pretty good. Gave up a couple solo homers, but no walks before it, so that was all right. He did a good job, it's just too bad he got hit by the foul ball, we just couldn't take a chance," Leyland said. "He should be OK for his next start."
In the sixth inning, Floyd escaped trouble again. He allowed a leadoff a double to Jackson. After he struck out Boesch, Floyd walked Fielder and Young to load the bases. He then ended the inning by striking out Alex Avila.
"He pitched great. He was aggressive early," Flowers said. "Most importantly I think the pitches that he missed he missed in good spots where they were effective setting up the next pitch."
Ramirez homered on a 1-2 pitch from Wilk in the second inning to give the White Sox a l-0 lead.
Flowers homered with two outs in the fifth inning. The ball landed deep into the left field seats. Flowers started at catcher to give A.J. Pierzynski a day off.
Flowers said the calming influence of new manager Robin Ventura has been a factor in the team's early success.
"I guess you can say that. We all know him, he is a little bit more laid back than most, but he has jumped us a few times when we needed to be jumped," said Flowers. "We play hard, I think we see that, we play as a team, more so since I've been here I think. Actually there has been a little more camaraderie and such going on in the clubhouse, on the field and in the dugout and I think that's better for the team. I think that ends up picking up everybody else when they struggle."
Wilk had a 5.40 ERA with no decisions in five relief appearances in 2011. He was added to the rotation after Doug Fister was placed on the disabled list Sunday with a left rib muscle strain.
The Tigers activated infielder Brandon Inge from the 15-day disabled list Saturday. He is expected to start at second base Sunday. Inge, who strained his groin during spring training, hit .197 with three homers and 23 RBIs in 103 games at third base last year. He grounded out in a pinch-hit appearance to end the game. ... Raburn stole a hit from Ramirez in the fifth by making a sliding, over the head catch down the right field line.