"It felt good to do that and get a 'W,'" Thome said.
Thome also tied a career high with four hits. His second homer in the last three games tied him with Hall of Famers Ernie Banks and Eddie Mathews for 19th place on the all-time list.
"There's a lot of respect for those guys and what they've done for the game," Thome said. "To be a part of that is special as well. It's very humbling to have those names mentioned because of the great players they were. To be on that list is pretty special."
Danks (2-1) allowed three singles for the White Sox, who have won 11 of their last 16 games. The left-hander has not given up a run in two straight starts, totaling 14 2/3 innings. It's the first time he has won back-to-back starts since last July.
"My goal is just not to be the guy I was last year," Danks said. "Last year I felt like I was the guy when someone would ask who's pitching and they would say me, it was kind of like 'Well, let me strap it on today, we've got to score.' I want to be the guy that the team knows that when I go out there we're going to hold them to three runs or less and I'm going to give them a chance to win."
Danks' first win of the season last Tuesday against Oakland snapped a personal 11-game winless streak.
"Their guy was really good," Rays manager Joe Maddon said. "Total command of all he was doing. He was really good today."
The Rays had just one runner in scoring position -- Carl Crawford reached third with two outs in the fourth -- against Danks.
Boone Logan pitched the final two innings for Chicago to complete a four-hitter.
Thome, who went 4-for-5, put the White Sox ahead 1-0 in the first with his fifth homer of the season. His third-inning RBI single off Edwin Jackson (2-2) made it 2-0.
Thome has totaled four hits in a game 10 times. The last time he accomplished the feat was Sept. 6, 2006, at Boston.
"Awesome," White Sox manager Ozzie Guillen said. "Jimmy can carry a ballclub. He just had to be patient. A lot of people were kind of worried about how Jimmy's going to do. We won a couple games on this road trip because of Jimmy. Everybody was rooting for Jimmy to have a good day like this."
Thome's batting average went from .172 to .222 Sunday.
Jackson gave up six runs and seven hits in 4 1/3 innings. The right-hander also struggled in his previous start Tuesday, allowing five runs and four hits over five innings in a 5-3 loss to the New York Yankees.
"I felt good today," Jackson said. "It's just one of those days you feel good and you don't get the job done. You have to have a short-term memory about it, and get ready to work and go into the next start."
After the game, the Rays added 1B Dan Johnson, who was claimed off waivers from Oakland, to the 25-man roster and optioned RHP Jeff Niemann to Triple-A Durham. ... White Sox 1B Paul Konerko, mired in a 4-for-32 slide, was rested. ... Tampa Bay ace Scott Kazmir (left elbow) had a bullpen session and will make his second rehab start Wednesday for Class-A Vero Beach. He is expected to rejoin the team around May 3. ... Tampa Bay SS Jason Bartlett, slowed by a tired throwing arm, was out of the lineup. The problem is not thought to be serious. ... Rays RHP Matt Garza (right arm irritated nerve) allowed four runs and eight hits over 3 2-3 innings in his first rehab start for Vero Beach. He could rejoin the rotation Friday. ... Pierzynski snapped an 0-for-11 slide with a single in the second. ... Tampa Bay RHP Al Reyes (shoulder) has resumed playing catch and could return from the disabled list on Apr. 30.