Although he intercepted only one pass in his rookie season in 1960, he went on to become the AFL’s all-time interception leader. In 1961, his first starting season, he snared nine passes and punted with a 40.7 yard average. In a tight defensive duel in the AFL Championship Game, his four booming punts helped Houston defeat the San Diego Chargers, 10-3, claiming their second AFL championship in as many seasons.
While nursing a slim half-game lead in the Eastern Division in Week 12 of the 1962 AFL season, Norton personally tormented Denver Broncos quarterback Frank Tripucka. He stopped three Bronco drives with interceptions as the Oilers stole a 34-17 victory and a berth in their third straight AFL Championship Game. That thriller for the 1962 AFL crown was the league's longest game, a double-overtime contest won by the Dallas Texans, 20-17.
As a defensive back, Norton was a steady tackler with a nose for the football. His play earned him All-AFL honors for 1961, '62, '63, and '67, when he scored the only touchdown of his career, returning an interception 56 yards. His number 43 was the first retired by the Oilers, acknowledging his club-record 45 career interceptions, which he returned for 592 yards and a touchdown, and 519 punts. The Oilers later retired the numbers of Elvin Bethea, Earl Campbell, Mike Munchak, Bruce Matthews, and Warren Moon.