The 5-foot-8 Sims scored on runs of 47, 11 and nine yards. He added 50 yards passing and earned offensive MVP honors.
His cousin, running back Herschel Sims, scored on a 60-yard run.
The cousins combined for 289 yards rushing and four TDs. When the final gun sounded, they embraced at midfield. Then a swarm of jubilant teammates mobbed them.
Abilene had not won a state championship since 1956.
Tigers quarterback Brooks Haack completed clutch passes and kept his team within striking distance until late in the game.
Katy's Donovonn Young scored from two yards out in the second period to cut Abilene's lead to one touchdown. Then Mikey Rodriguez kicked a 26-yard field to make it 14-10.
But the Eagles pressured Haack often and shut down his ground game. Star running back Will Jeffery managed 22 yards. The Eagles threw him for losses on three of his nine carries.
Abilene arrived averaging 45.6 points a game and took two plays to score. Herschel Sims ran 12 yards on the first play from scrimmage. A personal foul penalty added 15-yards, then Ronnell Sims ran 47 yards for a touchdown.
The Eagles threatened to blow the game open, building a 14-0 lead and driving to the Katy 11. But the Tigers held, knocking Ronnell Sims for a 1-yard loss on fourth-and-1, then driving 88 yards for their first score.
When Rodriguez followed with a field goal, the momentum had shifted.
Ronnell Sims, who rushed for 113 yards in the first half, suddenly found a wall of defenders. So did his cousin. The Eagles failed to make a first down on consecutive possessions. Katy smelled a comeback and drove to the Abilene 22. But the Eagles held, stole the momentum, and drove 78 yards in 10 plays to pull ahead, 21-10.