Toronto's lefty allowed two hits in seven scoreless innings Thursday night, sending the Blue Jays to a 2-0 win and their fifth straight victory.
"After that first inning I came in and said 'It's cold out there,'" Eveland said of the 45-degree temperatures on a windy night at U.S. Cellular Field.
"I was fortunate that the one ball that was hit well stayed in the yard," Eveland added. "Luckily I made him hit it a long way to center."
Eveland (3-1) outpitched Chicago's left-hander, John Danks (3-1), who also lasted seven innings.
The Blue Jays broke through against Danks with one out in the fifth when John Buck singled, Travis Snider doubled into the right field corner and Fred Lewis drove a two-run double into left center for a 2-0 lead.
"The main thing I was trying to get the ball out of the infield. There was great pitching on both sides, but something had to give and I came up with the big hit in the big situation," Lewis said.
"I made three mistakes to three batters in a row," said Danks after the White Sox slipped to five games under .500 in their disappointing start.
"As a whole we're just frustrated we're not winning more than we are," Danks said. "We're plenty talented, it's just a matter of us playing to our capabilities. I don't know how much longer they are going to give us to right this ship. ..."
But the White Sox are going to have to thaw out their bats before they fall too far behind in the AL Central.
Second-year second baseman Gordon Beckham, who batted .270 with 14 homers last year in a strong rookie season, went 0 for 4 with three strikeouts and also made two errors. His average dropped to .198 and manager Ozzie Guillen had a talk with his struggling young star after the game.
"I'm so frustrated with the way that I'm playing that it's gotten into my head mentally and it's causing my body to look like I don't want to be out there and that's not me," Beckham said.
"I've grown up knowing how to play the game the right way and I haven't been doing it in the last couple days."
Toronto's Scott Downs pitched a spotless eighth. Chicago's Alex Rios got a double when Blue Jays shortstop Alex Gonzalez couldn't hold his high pop behind second with one out in the ninth, but Kevin Gregg then struck out Carlos Quentin and Ramirez to get his eighth saves in as many chances.
"We were a little anxious at the plate," Guillen said. "We look like the weather in Chicago. "Play very good one day, very bad the next and then very good and then get cold."
Danks gave up eight hits and two runs in his seven innings. Sergio Santos pitched a scoreless eighth for Chicago and the converted infielder has still not allowed a run in his first 12 appearances -- a record for a White Sox pitcher starting his major league career, according to Elias Sports Bureau.
Eveland also beat the White Sox at Toronto in April. ... Major league home run leader Paul Konerko of the White Sox was scratched with a sore neck but is expected back Friday. Konerko has 12 homers. ... Blue Jays DH Randy Ruiz rejoined the team after missing the previous series for personal reasons. ... A fan ran on the field in the bottom of the sixth but instead of leading security on a long chase, he slid down in shallow right center and surrendered. ... The Blue Jays are now 10-3 on the road.