Willis gave up only one hit but walked seven in five-plus innings in his Tigers debut, and Detroit remained the only winless team in the majors with a 5-3 loss to Chicago on Saturday.
Detroit is 0-5 for the first time since the Tigers dropped their first nine games in 2003 en route to an AL-record 119 losses.
"We're a good ballclub. When I was here early, early in my career, those teams had to battle to just win a game," said Brandon Inge, who was on that 2003 team. "This team isn't like that. It's a good team and we're going through a little rough stretch right now."
"I was terrible and that's pretty much it," said Willis, obtained from Florida along with Miguel Cabrera in a six-player deal. "But you still have to battle and try and keep your team in the game."
Inge drove in all of Detroit's runs with a two-run homer and RBI double.
"Early in the game we couldn't get a hit off Willis, but kept runners on base with the walks," said Paul Konerko. "He was keeping us off balance. We kept our patience and the hits finally happened."
Willis was pulled in favor of Zach Miner (0-1). A groundout by Konerko made it 3-2. Miner then walked Jermaine Dye, and Carlos Quentin followed with a single to tie it. Center fielder Clete Thomas bobbled the ball for an error, which allowed Dye to continue to third. Joe Crede then hit a sacrifice fly.
"We believe that we can come back every game," said White Sox manager Ozzie Guillen. "We continue to fight back and never give up."
Dye added his homer with two outs in the eight.
Gavin Floyd (1-0) gave up three runs on six hits in six innings, walking two and striking out two.
"I struggled a bit and grooved one into Inge," he said. "But I was able to find myself and kept us in the game."
Bobby Jenks got his third save after putting runners on first and second with two outs. He induced Thomas to ground into a force play to end the game.
"I don't think anybody here should be pressing," said Tigers' manger Jim Leyland. "Maybe a little anxious, getting a little impatient at the plate."
Leyland said DH Gary Sheffield, who has missed two games with a torn tendon on a finger on his left hand, swung the bat on Saturday and felt good. The manager said there was a good chance that Sheffield would be back in the lineup for Sunday night's game. ... Floyd is 2-0 with a 3.03 ERA against the Tigers in five career starts. ... The Tigers optioned OF-IF Ryan Raburn to Triple-A Toledo and purchased the contract of RHP Francis Beltran. That gives Detroit 13 pitchers. Leyland said that was necessary because set-up man Fernando Rodney, who has been out with tendinitis in his throwing shoulder, experienced pain when he pitched a bullpen session on Thursday in Lakeland, Fla.