The British number three qualified for the tournament before overcoming the world number 29 Tiafoe to set up a second-round match with Lloyd Harris at the Florida event.
American Tiafoe cut a frustrated figure in defeat.
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"Very frustrating, very frustrating," said Tiafoe.
"I definitely shouldn’t have lost tonight. I probably rushed on big points, instead of working the point a little more."
The third-seeded Tiafoe looked to have the match against the qualifier in hand when he served up 6-5 and 30-love in the second set but was instead broken by Evans, whose aggressive net play frustrated Tiafoe in the final two sets as the Briton eventually prevailed 3-6 7-6(1) 7-5.
Late drama arose when Evans served for the match up 5-4 in the third set but nerves appeared to get to him and he was broken amid a flurry of unforced errors.
But Tiafoe was broken in the next game and Evans made sure not to make the same mistake twice, winning his final service game at love to set up a second-round match against tournament wild card Lloyd Harris of South Africa.
World number fourJuan Martin del Potro, who missed last month's Australian Open to nurse the kneecap he fractured at the Shanghai Masters, showed no ill effects in his first match of the year as he blasted 12 aces to see off baseline specialist Nishioka.
The hard-hitting Argentine is looking to pick up where he left off before the injury, when his superb play made him a finalist at the U.S. and China Opens and helped the 30-year-old reach a career-high ranking of world number three.
Del Potro, who won the tournament in Florida in 2011, will next face big-serving American Reilly Opelka after last week's New York Open champion saw off countryman Tennys Sandgren 6-4 6-0 earlier in the day.
Top American men's player John Isner used his blistering serve to overwhelm Canadian Peter Polansky 6-3 7-6(4) and advance to the second round.
The second-seeded Isner fired 23 aces to Polansky's four and won 87 percent of his first serve points as he cruised to victory.
Next up for Isner is a second-round meeting with unseeded Slovak Lukas Lacko on Wednesday.
Adrian Mannarino, Andreas Seppi, Paolo Lorenzi, Jordan Thompson, Steve Johnson, Mackenzie McDonald, Guillermo Garcia-Lopez and Radu Albot also won their first round matches on Tuesday at the ATP World Tour 250 event, which is played on outdoor hard courts.
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