The Longhorns' defense stifled the first-year Warriors and received a pair of rushing touchdowns from Tevin Abney in a key district game.
Lennard quarterback Fred Porter also accounted for two scores, rushing for one and connecting with DeMyco Winston for 30 yards.
The Longhorns are 3-5 and 2-4 in the district.
The Falcons came back from a 13-3 halftime deficit to win on Luis Rodriguez's 25-yard field goal in overtime.
Leto went into the half trailing by 10, but Fred Timmons returned the second-half opening kickoff for a touchdown.
Running back Jeremy Deering ran for 115 yards in the win.
Ed Encina, Times staff writer