Both players started strongly, with Del Potro serving powerfully while his opponent produced a stunning lob to prevent the Argentine from breaking.
It wasn't long though until the former US Open champion stamped his authority on the match by breaking the Ukrainian in the fourth game.
Dolgopolov fought back with a break of his own but Del Potro immediately regained control by winning two straight games to take the first set.
Just the one break of serve would decide the second, with the world number 11 displaying his greater experience against an opponent who was playing in only his second Masters quarter-final.
That made the score 3-2 and from then on it was routine for Del Potro, who wrapped up victory in an hour and a half.