The last-place Cubs struck out 17 times, running their total to 44 for the weekend series, but Rizzo and touted rookie Javier Baez had two hits apiece to key a 13-hit attack. Carlos Villanueva pitched a scoreless inning to earn the victory.
Baez struck out in the 12th, but reached on a wild pitch that moved Ryan Sweeney to third. Baez moved to second on another wild pitch by Cesar Ramos before Rizzo lined a single to right-center field.
The Rays lost for only the fifth time in their last 23 road games.