Rodriguez was named Florida's interim manager earlier in the day following the dismissal of Fredi Gonzalez, bench coach Carlos Tosca and hitting coach Jim Presley.
Both the homers by Sanchez and Cantu came in the third and rallied the Marlins from an early four-run deficit.
Florida took the lead with a two-run seventh -- the RBIs coming on a ground-rule double by Ronny Paulino and a two-base hit from Chris Coghlan. After Baltimore closed within a run in the eighth, Coghlan doubled home Paulino again in the ninth for an insurance tally.
Ricky Nolasco (6-6) was the winner, giving up four runs on eight hits with eight strikeouts in seven innings. Leo Nunez tossed a perfect ninth for his 16th save.
Brian Matusz (2-8) suffered the loss, surrendering six runs on seven hits in 6 1/3 innings.
Baltimore, which has won six fewer games than any other team in the majors, dropped its third in a row.
2014: The Year in Music [PHOTOS]