Francoeur singled off Joel Peralta (1-5) with two gone in the top of the 10th and went to second on shortstop Ben Zobrist's throwing error. That brought up Hosmer, who blooped a single in front of center fielder B.J. Upton, allowing the run to score.
Greg Holland followed in the bottom of the 10th with his sixth save and Kelvin Herrera (1-1) notched the win with a scoreless ninth.
Tampa Bay's David Price matched Hochevar with eight scoreless frames of his own. The Rays ace surrendered three hits, didn't issue a walk and fanned eight, tossing 80 of his 114 pitches for strikes.