The match got underway yesterday evening but was abandoned because of the wet conditions in New York with Djokovic leading the opening set 2-0.
When the pair returned to the Louis Armstrong Stadium this evening, Djokovic soon recorded another break of Wawrinka's serve to take command of the set.
His Swiss opponent managed to claim one of those breaks back, but it wasn't enough to prevent the defending champion from opening up a one-set lead.
The second set was dominated by Djokovic, who again broke Wawrinka twice on his way to wrapping up a 6-1 success.
Just before the third set got underway, Wawrinka called for a doctor and the trainer. Following a discussion, the Swiss player returned to the court.
However, with the score 3-1 in Djokovic's favour, Wawrinka decided that he could no longer continue because of a so-far-unspecified medical complaint.
As a result, Djokovic will now face either Juan Martin del Potro or Andy Roddick for a place in the semi-finals.