During his tenure at Arkansas, Broyles coached the Razorbacks to seven Southwest Conference championships, and two Cotton Bowl Classic wins. His 1964 team was proclaimed national champions by the Football Writers Association of America, as well as the Helms Foundation, and to date is the last Razorback team to go undefeated and untied in a season. If the wire service polls had not given out their national championships prior to the bowl games during that era of college football, Arkansas positively would have won both the AP and the UPI national titles as well, since Alabama (winner of both) lost to Texas (a team Arkansas beat in Austin in 1964) in the Orange Bowl. He still holds the record for most wins by a head coach in the history of Arkansas football, with 144. During the 1960s and 1970s, one of college football's most intense rivalries was between Broyles' Razorbacks and the University of Texas Longhorns under legendary coach Darrell Royal.