Wawrinka, last year’s Australian Open winner, struggled until breaking loose with his big game in the final set as he defeated Guillermo Garcia-Lopez 6-7 6-4, 6-2 for his second win over the Spaniard in three weeks.
Earlier, Murray saved five break points to hold off Canadian Vasek Pospisil 6-3, 7-5 and reach the last eight.
Wawrinka had his problems against Garcia-Lopez, whom he beat at the Australian Open last month, a tiebreaker deciding a 63-minute opening set. The Swiss regrouped and took the second set before running away with the third to stay alive in an event he last played a decade ago.
He said: “It was a good match with a lot of intensity. It was a tough battle. I???m happy with how I’m playing, generally I’m feeling good here. The first two sets were very intense. But I was playing a bit passive. After the second set I increased my aggression and relaxed a bit and started playing better.”
Third-seed and defending champion Tomas Berdych reached the last eight at the Ahoy Stadium with a defeat of Italian Andreas Seppi 6-0 3-6 6-3.
Berdych swept the opening set before being made to work in the second as Seppi levelled. The Czech finally prevailed thanks to a break midway through the final set, running out the winner on his first match point.
Berdych said: “Andreas played very well in the second set. For me it was about trying to play like I had in the first set. I was still able to finally win in the end.”
Second seed Milos Raonic came through safely in the last of the second-round matches, seeing off Italy’s Simone Bolelli in straight sets, 6-3 7-6.