In the 1984 Sun Bowl, with Tennessee down 28–27, Robinson led a late drive into Maryland territory, but lost the ball on a fumble, allowing the Terrapins to escape with the win. Robinson finished the 1984 season with 153 completions on 256 passes for 1,963 yards, 14 touchdowns, and 9 interceptions, falling just short of Alan Cockrell's school single-season record of 2,021 passing yards. He also rushed for 126 yards and 3 touchdowns, giving him a school-record 2,089 yards of total offense. His 61.7% completion rate also set a record, surpassing Johnny Majors' 1956 mark of 61.3%. Robinson was named Preseason All-SEC prior to the 1985 season. He was also considered a contender for the Heisman Trophy. In Tennessee's season opener against 10th-ranked UCLA, he threw for a school record 387 yards and two touchdowns, including a 68-yard bomb to Clinkscales, and rushed for 30 yards, giving him 417 total yards to break his own school record for total offense. The Bruins rallied to score 16 points late in the fourth quarter, however, to escape with a 26-26 tie. On September 28, 1985, Tennessee hosted #1 Auburn, which featured eventual Heisman winner Bo Jackson at running back. On Tennessee's first drive, Robinson broke loose for a 39-yard scramble to set up the Vols' first score. Following an Auburn turnover, Robinson connected with McGee for a 37-yard touchdown. In the second quarter, Robinson engineered a third scoring drive, capped by an off-balance touchdown pass to Vince Carter. When Auburn cut the lead to 24–6 in the fourth quarter, Robinson led the Vols downfield on another scoring drive, which featured a long pass to McGee and a touchdown pass to Clinkscales. After Auburn scored again, Robinson responded with a 30–yard touchdown pass to Eric Swanson, and the Vols held on for a 38–20 win. Robinson finished with 259 yards passing and a school-record four touchdown passes. Having upstaged Jackson, Robinson was featured on the cover of the October 7, 1985, edition of "Sports Illustrated" under the caption, "The Tennessee Waltz: Tony Robinson Buries Auburn." After a hard-fought victory over Wake Forest, Tennessee traveled to Gainesville to face the #7 Florida Gators, who had not lost since the first week of the 1984 season. Robinson completed 26 of 36 passes for 300 yards, but managed just one touchdown pass—a 20-yarder to McGee in the fourth quarter—as the Florida defense successfully executed a "bend-but-don't-break" strategy.