Evans, 23, qualified for the main draw for the first time, but was widely expected to go home soon afterwards having been drawn against the Japanese number one, who as world number 12 is ranked 167 places above the Briton.
But the Birmingham-born world number 179 made light work of Nishikori, winning through in just under two hours for his finest career victory.
He will next face Bernard Tomic in the second round after the Australian overcame Alberto Ramos 6-3 3-6 4-6 7-6(1) 6-3.
"It's definitely a good one," said Evans. "That was pretty good out there to play so well and against someone so highly ranked.
"I felt pretty confident all through the week, and that was a good match. I wasn't worried."
Evans was off the radar until April, when he was surprisingly selected for the Davis Cup tie with Russia, despite being outside the top 300 at the time.
He impressed as Britain won 3-2, and has gone on to show good form on the ATP and Challenger tours, reaching two finals in the men's second tier and breaking into the top 200.
His only two previous Grand Slam appearances came as Wimbledon wild-cards, so this was his first qualification for a Major by right.
But, despite coming through qualifying, he was not seen as a realistic contender against Nishikori. This win firmly puts Evans on the map.