Ramsey, who completed 21 of 31 passes, has thrown for 17 touchdowns this season and has at least two in all six of Tulane's games.
The Green Wave (2-5, 1-2 C-USA) opened the scoring on Ramsey's 39-yard pass to Chris Coleman with 4:17 left in the first quarter, then erupted for 24 points in the second period to open a 31-14 halftime lead.
Mewelde Moore rushed for 88 yards and a touchdown on 21 carries for Tulane, which rebounded from last week's 46-33 setback to Cincinnati.
The Horned Frogs (3-3, 1-1) tied the contest on Jason Goss' 50-yard punt return 15 seconds into the second period, but Ramsey three touchdown passes in less than five minutes.
He found Royde Williams for a 46-yard score with 12:48 left in the half, then threw scoring strikes of 11 of 44 yards to Terrell Harris to give the Green Wave a 28-7 lead.
Sean Stilley completed 15 of 32 passes for 158 yards and three touchdowns for Texas Christian.
Corey Connally rushed for two touchdowns for the Horned Frogs, but was held to 74 yards on 19 carries after gaining 199 yards in last week's 34-17 victory at Houston.