The number five seed settled into a rhythm on the Belgian's serve to break him twice, although the 27-year-old hit back with a break of his own.
However, Wawrinka took the attack to Bemelmans on his serve once more to secure the break that clinched him the first set 6-3.
Both men improved their groundstrokes in the second set and the Belgian was resilient on his serve, repelling the aggressive play of the two-time Grand Slam champion to send the match to a tie-breaker.
Wawrinka upped the ante, though, and managed to edge a tight contest due to the quality of his play in the key moments to take it 7-5 to secure the second set.
The Swiss began to look at his best on the court as he dominated the rallies in the third and earned an early break to put the pressure on the Belgian.
Wawrinka looked to have sealed his victory when he broke Bemelmens for the second time in the third, only for the 27-year-old to hit back in the next game to keep his hopes alive. However, the Swiss eventually overcame the spirited play of Bemelmans to earn his place in the last 16.
The Swiss will now face American Donald Young in the fourth round of the competition.