The Cubs, who had not lost since being swept by the Milwaukee Brewers in a three-game series in Chicago on Sept. 8-10, are scheduled to open a four-game series in Milwaukee on Thursday night. They held a 3 1/2-game lead over the Brewers entering Wednesday.
Steven Souza Jr. hit his 30th home run in the first inning and the Rays added three more runs in the second off Jon Lester.
Wilson Ramos, who had three of Tampa Bay's 10 hits, made it 7-0 with a two-run single in the fifth that knocked Lester (11-8) out of the game.
Lester, who had won three starts since coming off the disabled list on Sept. 2, gave up seven runs and eight hits with three walks in 4 1/3 innings. He had no strikeouts.
Snell (4-6) gave up singles to John Jay in the third and Addison Russell in the fifth. He walked three and struck out five in seven innings. Snell is 4-0 in 10 starts since July 24.
