The Rays' matched the 2003 Kansas City Royals for the hottest streak to start a season in baseball's wild-card era.
The Rays' plus-57 run differential through nine games is the largest ever in MLB since 1900.
Padres starter Seth Lugo (2-0) gave up one run on five hits and four walks with five strikeouts over six innings to earn the win.
Chicago starter Michael Kopech (0-2) gave up one run and two hits in six innings, with three walks and five strikeouts.
Rangers starter Jon Gray (1-1) allowed Edwin Rios' two-run homer in the second inning.