The veteran striker was named in the Manchester United starting line-up for the second successive Premier League game for the visit of Southampton in the mid-week clash.
Aaron Wan-Bissaka broke the deadlock in the 18th minute before Marcus Rashford scored his 83rd goal for the club midway through the first half at Old Trafford.
Jan Bednarek scored an own goal under pressure from Rashford before Cavani scored his fifth Premier League goal of the 2020-21 season ahead of the half-time break.
Cavani was withdrawn at half-time after he suffered a knock to his ankle and his replacement Anthony Martial scored twice in the second half at Old Trafford.