Boise State, which finished the season with a perfect 14-0 record, intercepted a pass to kill a late rally by the Horned Frogs.
Martin's game-winner came with 7:21 to play. The Broncos also scored on a 50-yard interception return by Brandyn Thompson and a 40-yard field goal by Kyle Brotzman.
Andy Dalton connected with Curtis Clay on a 30-yard touchdown pass and Ross Evans kicked a 29-yard field goal for TCU (12-1).
Kellen Moore completed 23-of-39 passes for 211 yards for Boise State, which joined the 2002 Ohio State Buckeyes as the only NCAA teams to finish a season 14-0.
Dalton was 25-of-44 passing for 272 yards and the touchdown, but was picked off three times.