Ryan Newsome and Taco Anderson scored two touchdowns apiece for Aledo.
It was the fourth state title in five years for Aledo (16-0). That stretch began with a win over Brenham for the 2009 championship.
Aledo became the first team to score 1,000 points in a season, according to the National Federation of State High School Associations. Newsome's 28-yard scoring catch from Bishop 59 seconds before halftime put Aledo over 1,000 points.
Aledo finished with 1,023 points after its second-lowest scoring total of the season. Aledo had 29 points in a state semifinal win over Ennis.
Chance Navarez had five PAT kicks to increase his national season record to 132 points.
Caleb Hill threw for 216 yards and a touchdown with an interception for Brenham (14-2).
The national scoring record going into the season was 901 points by Albemarle, N.C., in 2001, also in 16 games. The Texas record was 891 by Refugio in 15 games in 2011.
Bishop, the offensive player of the game, was 6 of 10 passing for 157 yards and had a game-high 133 rushing yards on 13 carries. The junior finished the season with 37 TD passes.
Brenham held Aledo to a field goal in the first quarter, and had a chance to take the lead from the Aledo 2. But confusion on a handoff from Hill to Earnest Patterson led to a fumble recovery by Aledo.
Brenham pulled even at 3-all on Tein Pham's 22-yard field goal midway through the second quarter.
Aledo needed just three plays to break the tie on Daythan Davis' 2-yard touchdown run.
Aledo scored on the first play in the fourth quarter on a 43-yard pass from Bishop to Anderson. That was the first of three fourth-quarter touchdowns.
Jess Anders rushed for 119 yards for Aledo, and Anderson had four catches for 95 yards. Aledo had 513 yards total offense.
Brenham scored its only touchdown with 7:55 to play on a 70-yard pass from Hill to Tre'Vonte Johnson. The ball was nearly intercepted, but it went between a defender's hands.
James Homas, Brenham's leading receiver, left the game after taking a hard hit in the first quarter. He caught two passes for 42 yards.
Brenham has lost in all three trips to the state finals in the past 12 seasons.