Matches on the outdoor courts were suspended for three hours as temperatures reached 35 degrees at Melbourne Park.
At the time of the suspension, Evans was leading by two sets to one against Facunado Bagnis.
When the players returned to court, Evans won the fourth set and the match 6-4, 4-6, 6-4, 6-4.
Evans needed to use an ice pack on his head to keep himself cool in any break in the match. He now has a much-needed day off before facing Jeremy Chardy in the second round.
The 32-year-old is the second British man into round two following Cameron Norrie’s success in his match on day one.
Norrie faces France’s Constant Lestienne on Wednesday for a place in round three.