The French Open champion and winner of two of the last six Grand Slams strolled off court after clinching victory in one hour and 31 minutes.
The fourth-seeded Swiss player has only once reached the quarter-finals at Wimbledon, losing to compatriot Roger Federer in 2014, and will face Spaniard Fernando Verdasco in the third round on Friday.
Dominican Estrella Burgos, who had never won back-to-back matches on grass, was broken once at the tail-end of each set.
“He’s a tough player,” Wawrinka told the BBC. “I didn’t know exactly what to expect, but I’m happy to get through in three sets. There are a lot of things I would like to be doing better but it’s important to get through.”
Things weren’t quite as simple for the 10th seed Marin Cilic on Wednesday. A double fault by the narrowest of margins allowed the US Open champion to complete a great escape with a five-set victory over Richard Berankis.
The Lithuanian journeyman appeared to be on the verge of pulling off a shock upset when he held two break points at 5-5 in the fifth set.
But Croatian Cilic saved the first with a forehand winner and blew out his cheeks in relief when he saw Berankis’ forehand drop long on the second.
One game later it was all over as Hawkeye confirmed Berankis’s second serve at match point down missed the line by millimetres, allowing Cilic to win 6-3 4-6 7-6 (8-6) 4-6 7-5 and book a third-round clash with American John Isner.
Isner beat Australian wildcard Matthew Ebden 6-2 7-6 6-4 in a match that took less than two hours but was marred by a ballboy being taken ill in the high heat. ?? ?? ?? ?? ?? ??