At the Rogers Cup in Toronto, the Aussie raced to take the first set, but Wawrinka won the next two to seal the match 1-6 7-5 7-5.
The Serbian star, who last won the Rogers Cup in 2016 and is coming off a win at Wimbledon this year, will next face wild-card Peter Polansky of Thornhill, Ont.
"I thought I served well in the moments when I really need it", Djokovic said.
Citi Open champion Zverev continued his good form with a straightforward 6-4 6-4 win over Klahn. Overall, my game was so-and-so. "I just patiently waited for the moment and it happened".
Djokovic, the ninth seed, was originally scheduled to play Australian Open semi-finalist Chung Hyeon but the 22-year-old South Korean withdrew with a back injury about an hour before the match was due to start.
Meanwhile, Wimbledon champion Novak Djokovic swept aside lucky loser Mirza Basic, winning 6-3 7-6 (7-3).
The two traded hot shots across almost three hours with Nadal edging the Swiss, 7-5, 7-6 (4). Haase beat Mikhail Youzhny of Russian Federation 7-5, 6-2.
Rafael Nadal did his part to put Rogers Cup schedule back on track with a speedy 6-2 6-3 win over Frenchman Benoit Paire on Wednesday.
Other winners were Bulgaria's Grigor Dimitrov who defeated the American Frances Tiafoe 7-6 (1), 3-6 and 7-6 (4) and Croatia's Marin Cilic who defeated Argentina's Diego Schwartzman 6-3 and 6-2, making him Nadal's next rival.
"I hear all kinds of (pronunciations), like obviously in English "ogre" is always present", Auger-Aliassime said with a laugh.
Toronto's Daniel Nestor - the oldest player at the tournament at 45 - and Vancouver's Vasek Pospisil lost to Feliciano and Marc Lopez 6-7 (8), 6-2, 10-6.
The inclement weather also forced Shapovalov to wait, but the Canadian had no issues dispatching Chardy 6-1 6-4.
'I knew I was playing pretty good today, ' a delighted Tsitsipas said.
"Sorry to my fans in Toronto, but I have to pull out of the tournament since my left wrist needs some days of rest", del Potro said in a tweet. That's what I needed, a match like this to be a little bit more confident and I did it".
Play was also suspended in the match between world number one Simona Halep of Romania and Russia's Anastasia Pavlyuchenkova.
Denis Shapovalov didn't hide his disappointment when he saw that his Wednesday afternoon match against Fabio Fognini had been moved from centre court to the grand stand. Djokovic had nine aces and was good on 76 per cent of his first serves, converting 76 per cent of his first service points and 79 per cent of his second service points. "And now that the tournament is here, it's like I have another priority".