Jose Tabata and Starling Marte each clubbed a three-run homer and drove in four, as Pittsburgh decimated Toronto by a 22-5 count in Grapefruit League action.
Tabata went 4-for-4 and scored twice, while Marte finished 5-for-6 and also scored two runs for the Pirates, who only failed to score in the opening inning and put up multiple runs during the second, fourth, sixth and seventh frames.
Rodriguez worked 4 2/3 innings for the win, allowing six hits and three runs despite four walks.
His counterpart J.A. Happ was yanked before recording an out in the fourth, charged in defeat with 12 hits and seven runs, striking out three.
Matt Tuiasosopo hit a solo homer, Dan Johnson, Ricardo Nanita and Sean Ochinko knocked in a run each for the Blue Jays.