Perkins's rebound basket with eight seconds to go cut the lead to three points before Porter put the game out of reach from the foul line.
The second time was with 6 minutes 2 seconds to play when Martin Salley's rebound basket made it 70-69.
Reid started a 17-4 scoring charge with an offensive rebound basket with six minutes left in the game.
Arkansas still led, 62-57, with 12:10 remaining after a rebound basket by forward Todd Day.
Johnson put the Privateers (24-2, 18-0) ahead by 50-49 on a rebound basket with 1:41 to play.
Battle put Illinois ahead to stay at 43-42 with a rebound basket with 13 minutes 15 seconds left in the game.
Fleming, who had 20 of his 24 points in the second half, put Indiana ahead, 119-117, with a rebound basket.
Then Barkley finally broke the ice with a rebound basket of his own.
Rhodes followed with a rebound basket, free throw and 3-pointer for a 48-32 advantage with 18:20 left in the game.
"And that is to eliminate the offensive rebound basket," he said.