Broussard raced down the sideline on the first play of the second quarter after Alvin Dunn intercepted a George Malauulu pass.
Defensive back Richard Holt dragged down Broussard 10 yards from the goal line and the Cougars had to settle for a field goal.
"The biggest key for the defense was stopping the run," Arizona Coach Dick Tomey said after No. 22 Arizona held off the No. 15 Cougars, 23-21, Saturday in a Pacific 10 Conference game.
Washington State "did some damage late and had two key plays, but Richard Holt did an unbelievable job of running Steve Broussard down from behind."
Arizona, 5-2 overall and 4-1 in the conference, kept its Rose Bowl hopes alive by holding the Cougars (6-2 and 3-2) to 67 yards rushing and intercepting four passes from Aaron Garcia, who was sacked six times.
Darryl Lewis had two interceptions, and the second came with 1:37 left in the game after the Cougars had driven to a first down at the Arizona 27. Garcia was sacked the play before and hit by a blitz when he threw the interception on third and 20.
Jeff Hammerschmidt's interception set up Doug Pfaff's third field goal, a 28-yarder that put the Wildcats ahead 23-19 with 5:03 left. Washington State registered a safety with seven seconds remaining when Arizona punter John Nies ran out of the end zone.