Kenny Hall scored 13 points to lead a 56 victory over 13th-ranked Florida in the SEC opener Boling Arena.
Martin is in his first year at the helm after taking over for the fired Bruce Pearl and the Vols (8-7, 1-0 SEC) had lost each of their first three games against ranked opposition this season.
However, Tennessee never trailed in the second half on Saturday and kept Florida (12-4, 0-1) winless in true road games this season. The Gators are 0-4 in opponents' buildings, including previous losses to Ohio State, Syracuse and Rutgers.
Trae Golden and Jeronne Maymon each scored 12 points for Tennessee, while Jordan McRae chipped in 10. The Vols shot 51 percent overall and held Florida to just 35.7 percent from the field.
Erik Murphy and Kenny Boynton each finished with 13 points to lead Florida, which had won two straight since a double-overtime loss at Rutgers on December 29.