The fourth seed prevailed 7-6 (7/2), 6-4, 4-6, 7-6 (10/8) in just over three hours and will play Japan's Kei Nishikori in the last eight.
Garcia-Lopez, who knocked Wawrinka out in the first round at last year's French Open, held four set points at 6-2 in the tiebreaker to take the match into a fifth set before the Swiss star roared back.
Wawrinka had match point at 7-6 before the Spaniard got a fifth set point only to again be denied. He then clinched it on his second match point.
"I had to focus on every point. I knew if I was going to come back at 6-5, he was going to get nervous. I did a good passing shot, along the line. I just focused point after point."
Wawrinka looked to be strolling to a straight sets victory before Garcia-Lopez launched his fightback on Margaret Court Arena.
"I made maybe two mistakes then he started to play a little bit faster, a little bit more flat," Wawrinka said.
"I started to be on my defensive a little bit too much. But I'm happy to get through. It was important to win that match again. It's great for me to be in quarter-final and still be in it."
"I'm not focused on winning a major. I'm taking it match after match," he insisted.
"I know it's difficult to do it. It's amazing I already did one. I'm just happy to still be here playing great tennis so far.
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