Part of the 1959–60 bowl game season, it matched the independent and top-ranked Syracuse Orangemen and No.

[3][5] The Orangemen had just completed a perfect season for the first time in their history and were declared national champions by both major polls.

The Longhorns opened with eight wins and were co-champions of the Southwest Conference; after a late-season home loss to rival TCU, they dropped from second to fourth in the rankings.

This was the first Cotton Bowl appearance for third-year head coach Darrell Royal and the first for the Longhorns in seven years.

Jack Collins caught a 69-yard pass from Bobby Lackey to narrow the lead 1:46 into the third quarter, but the conversion failed, making it only 15–6.