Thome connected in the third inning for a three-run shot off rookie Jeff Niemann, who was making his second career start. The next batter, Paul Konerko, homered to make it 4-0.
The White Sox designated hitter tied Hall of Famer Mel Ott for 21st place on the all-time list with his fourth homer of the season, which hit an overhanging catwalk. Thome has reached base safely in all 26 games he has played at Tropicana Field.
Vazquez (3-1) gave up two runs and six hits over 6 1-3 innings for the White Sox, who have won 10 of their last 14 games. He struck out four with a walk.
The White Sox have out-homered their opponents 24-5 this season.
Chicago scored four more times in the fourth to extend its advantage to 8-0. Juan Uribe hit an RBI double, Orlando Cabrera had a run-scoring single, Konerko drove in a run when he was hit by a pitch and Jermaine Dye added a sacrifice fly.
Niemann (1-1) allowed eight runs - five earned - and five hits in 3 1-3 innings. He struck out one and walked four.
Uribe gave Chicago a 9-0 lead on a fifth-inning RBI single.
Evan Longoria, who earlier in the day agreed to a $17.5 million, six-year contract that could be worth up to $44.5 million over nine seasons, had an RBI grounder in the sixth. Jonny Gomes added a run-scoring double that ended Vazquez's stretch of scoreless innings at 15.
Notes:@ Rays ace Scott Kazmir (left elbow) allowed one run, one hit and struck out three over three innings in his first rehab start for Class-A Vero Beach. He could rejoin the team early next month. ... White Sox 3B Joe Crede was rested. Manager Ozzie Guillen might give several players a day off during the three-game series on artifical turf. ... Rays 1B Carlos Pena was out of the lineup with right hamstring tightness. He took batting practice and might DH Saturday.
