In the first matchup between the pair, Wawrinka only appeared temporarily in difficulty in the third set against Burgos, who at 34 is one of the older players at the All England Club.
“He's a good player, a tough player,” Wawrinka told media afterward.
“For me, it is important to get through,” the 30-year-old Lausanne native said.
“There are lots of things I want to work on, improve, but my game in practice is really good,” he said.
“It was a great match and I'm glad I'm through in three sets.”
French Open champion Wawrinka will next face Spain's Fernando Verdasco, ranked 43rd in the world.
Verdasco has beaten the Swiss player in two out of three outings and Wawrinka acknowledged he faces a formidable challenge on Friday.
“He's a really dangerous player.”