The fourth seed faced down Copil's rockets, including the fastest recorded serve so far this year, clocked at 242 kph (150 mph), on the way to his win in three tight sets.
Wawrinka won 7-6 (7/4), 7-6 (7/4), 6-3 in two hours, 16 minutes and will now play Finnish journeyman Jarkko Nieminen in the seeded round.
Copil kept Wawrinka on his toes with his lively serving and the Swiss needed two tiebreak sets to get the edge over the Romanian.
"It was quite a tough match and happy to get through, especially in three sets," Wawrinka said.
"The condition wasn't easy today. Quite hot. Really fast on the court and he was playing great. He was serving big, putting lots of pressure on me.
"I wasn't playing my best tennis, but I'm happy the way I fight today and win the match."
Wawrinka, who upset Rafael Nadal in last year's Melbourne final to win his maiden Grand Slam title, was satisfied two matches into the tournament.
"Yeah, I'm happy with my game in general," the Lausanne native said.
"To win first two matches in three sets, it's great."
Copil may have been ranked 190 spots below Wawrinka but in the end only four points separated the pair over the course of the match on Margaret Court Arena.
"It was important to take the first tiebreaker and I tried to stay aggressive with my game," Wawrinka said.
"He gave me a few points in the second tiebreaker."
It was far from the perfect match for Wawrinka as he made more unforced errors than winners at 39 to 36.
The Swiss could only get two breaks in seven opportunities on Copil's big serve.