Allen completed 18 of 29 passes for 316 yards and connected with Smith five times for 173 yards and two scores. Their 86-yard connection gave the Texans a 27-21 lead with 10:18 left in the third quarter.
Meanwhile, Derrel Kelley III rambled for 161 yards on 21 carries for Tarleton (2-1).
For his part, North Alabama (1-2) running back ShunDerrick Powell amassed 209 yards on 13 carries and scored three TDs. His 55-yard scoring run just before halftime gave the Lions their last lead of the contest at 21-20.
Powell finished 42 yards shy of the school rushing record he set against Division II-level UVA Wise on Sept. 10.