The third-seeded Australian Open champion defeated Uzbekistan's Denis Istomin 6-3, 6-3, 6-4 to reach the fourth round for the first time since 2009.
But the match should have been played Saturday before it was cancelled due to the torrential rain which swept the All England Club.
Wawrinka will now play his fourth round on Tuesday against 19th seed Feliciano Lopez of Spain who also waited until Monday to see off John Isner, the ninth seeded American, 6-7 (8/10), 7-6 (8/6), 7-6 (7/3), 7-5.
However, the top half of the draw, featuring top seed Novak Djokovic and defending champion Andy Murray, was completed on Saturday while Wawrinka's main title rivals in his section, Rafael Nadal and Roger Federer, also finished their third rounds two days ago.
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"I was disappointed. I was expecting them to move matches, move maybe juniors or doubles, to make my match or Isner/Lopez's match first on when they started at 5:00pm or 6:00pm again when it stop raining," said Wawrinka.
He added: "I was surprised because (after the rain) it was a perfect day to finish. They said for security reason, they didn't want to put our match on a small court. But (Kei) Nishikori (the 10th seed) was playing on small courts."
In the remaining third round match to be completed, Nishikori saw off Italian lucky loser Simone Bolelli 3-6, 6-3, 4-6, 7-6 (7/4), 6-4 after the pair had finished 3-3 in the decider on Saturday.