The Serb came through 7-6 6-3 6-1, overcoming the spirited American, whose resistance decreased as the match went on.
Both men comfortably held their opening service games, before Reynolds was forced to save a couple of break-point chances in the fourth game of the opening set.
He duly did, and eventually managed to force himself into a tie-break despite some Djokovic pressure at 5-6. The world number one showed his class thereafter, racing into a 5-0 lead, and then taking the tie-break 7-2 on his own serve.
Reynolds doggedly held on to his own serve in the opening game of the second set, but could not stop Djokovic moving 3-1 ahead. The Serb broke again in the final game to take a two-set lead.
By the third set Reynolds had little left to trouble his opponent as Djokovic moved through the gears and into a 4-1 lead. He broke his opponent again and served out the match in comfortable fashion.