Jennings finished 3-for-4 with two runs scored and Carlos Pena added a solo homer for Tampa Bay, which spilt a four-game series.
Price (17-5) rebounded from a poor performance in his previous start to become the American League's first 17-game winner, holding the Blue Jays to a pair of runs on six hits over 6 2/3 innings.
The left-hander overcame four walks and struck out five for Tampa Bay, which came into the contest 1 1/2 games out of an AL wild card spot.
Toronto's Ricky Romero (8-13) lasted only one full inning en route to losing his 12th straight decision, surrendering seven runs on eight hits.
Edwin Encarnacion connected for his 37th homer -- a two-run shot -- in the Blue Jays' loss.
Notable deaths of 2014 [PHOTOS]
UPI Sports Results for September 19, 2014