Wozniacki - who could return to the top of the world rankings if Simona Halep fails to make the last eight in Rome - triumphed 6-1 6-4 on Thursday (AEST), having been handed a bye in round one.
The Dane certainly did not have things all her own way, but Van Uytvanck was ultimately punished for taking just two of the nine break points that came her way, as Wozniacki converted five out of nine to set up a meeting with Anastasija Sevastova.
Both players faced break points in their opening service games, yet Wozniacki was the one who took her chance and she soon broke again to open up a 4-0 lead.
Although Van Uytvanck enjoyed sporadic success with the drop shot, it was not enough to prevent her opponent from easing through the remainder of the first set.
Wozniacki gave up an early lead in set two, however, she battled hard to regain the upper hand and finished things off in style with a love hold.