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.
Hurdle beat out Don Mattingly of the Los Angeles Dodgers and Fredi Gonzalez of the Atlanta Braves for the NL honors.