The world number 40's powerful serve was the difference on a sunny and windy day in Indian Wells as he won 83 percent of his first service points and fired down seven aces to beat Briton Evans, losing finalist at Delray Beach last month.
Three-times Grand Slam champion Wawrinka saw his ranking go into freefall following knee surgery in late 2017 and he finished last year as number 66 in the world.
The Swiss said he was feeling more confident after reaching the title-decider at last month's Rotterdam Open, his first final since the operation.
"It was great to make the final there and win those matches against the top players," the former world number three told reporters after the match.
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"But every tournament is a new tournament. You need to start from the beginning," he added. "Today was a tough match against a tough player in tough conditions."
Next up for Wawrinka is Hungarian 29th-seed Marton Fucsovics, who the 33-year-old has defeated in two of their three career meetings.
Feliciano Lopez came out on the winning side of two tie breakers for a 7-6(3) 7-6(2) victory over Tomas Berdych in his first round match.
In a battle of two tour veterans, Lopez's 15 aces and sharper execution in the tie-breakers gave him the edge. The Spaniard will next play 12th seed Karen Khachanov.
American Steve Johnson, German Peter Gojowczyk and 19-year-old Australian Alexei Popyrin were among the other first-round winners on Friday.
(Reporting by Rory Carroll, editing by Nick Mulvenney)
