Francona got the American League nod after guiding the Tribe to their first playoff appearance since 2007, edging out Boston skipper John Farrell, who led the Red Sox to a World Series title.
Francona took the AL honors with 16-of-30 first-place votes from baseball writers, while Farrell received 12 first-place votes and 2012 winner Bob Melvin of Oakland Athletics garnered a pair of first-place votes.
Cleveland had lost 94 games in 2012, but improved to 92-70 before bowing to Tampa Bay in the AL wild-card game.
Hurdle claimed the NL award after taking the Pirates to their first winning record and post-season appearance since 1992, engineering a 15-victory improvement over 2012.
The Pirates claimed a second-place finish in the NL Central with a 94-68 mark, beating the Cincinnati Reds in the wild-card game before falling to the St. Louis Cardinals in the NL Division Series.