In his final season in 1959, coach Ara Parseghian led the Wildcats to 6-0 record and were nationally ranked, defeating Oklahoma, Iowa, Minnesota, Michigan, Notre Dame and Indiana, before dropping their last three games to go 6–3.

He and the Oilers won the first AFL championship game on New Year's Day, 1961 over the San Diego Chargers, 24-16 before a crowd of 32,183 in Houston, Texas, led by quarterback George Blanda and flanker Billy Cannon, who hooked up on an 88-yard touchdown pass.

Later that same year, on Christmas Eve, the same two teams met for the 1961 AFL championship before a crowd of 29,556 in San Diego, where the Oilers prevailed 10–3.

Going for three championships in a row, the Oilers ended up losing to the Dallas Texans (who next year became the Kansas City Chiefs) in the longest title game in American pro football history.

It took two overtime periods in Houston before the Texans came away with a 20–17 victory on a 25-yard field goal by Tommy Brooker.