Philadelphia (6-5-4) moved into a third-place tie with Houston and Kansas City in the Eastern Conference.
Carroll scored from long distance in the 25th minute on a shot that was deflected as it sailed past goalkeeper Andy Gruenebaum.
Carroll then headed a corner kick to Sheanon Williams, who finished the play with a goal in the 29th minute. Conor Casey concluded the scoring 2 minutes later. It was the fourth shutout of the year for the Union.
Columbus is winless in its last three games and stayed stuck on 17 points, good for seventh place in the East.