Evans, who had never won more than one match in qualifying at a grand slam before arriving in New York, has now won five in a row to reach the third round.
He built on three qualifying victories and a first-round win over 11th seed Kei Nishikori by recovering from a set and a break down to defeat Tomic 1-6 6-3 7-6 (7/4) 6-3.
Evans then revealed that last year at the Masters tournament in Miami he had been due to practise with Tomic only to be told to leave by the Australian's father John.
It was not something the 23-year-old from Birmingham forgot, and revenge must have tasted sweet.
"I was there playing qualies," said Evans. "His dad sort of fobbed me off and said I wasn't good enough to practise with him. I remembered that.
"We went to practise, it was all booked. I got to the court. His dad said, 'No, no, he's a qualifier, I'm not hitting with you.' It was a bit embarrassing."
Things did not start promisingly for Evans on Court 17 as 20-year-old Tomic raced through the first set in 22 minutes.
Evans was serving double faults and spraying his forehand, and it looked like the match could go away from him quickly when Tomic broke for 2-1 in the second set.
But Evans broke back straight away, and that proved to be the turning point of the match.
He surged into a 4-2 lead, and got the better of three consecutive breaks to leave himself serving for the set.
He needed four chances, finally clinching it when the Australian put a backhand wide.
Evans, full of confidence after winning 12 of his previous 14 matches, was the player showing aggression and taking the game to Tomic, who is ranked 127 places higher at 52.
The third-set tie-break was the most important game of the match, but Evans was nerveless, powering away forehand winners to take it 7-4.
He was briefly a break down in the fourth set but won four games in a row, and served two aces in the final game before taking his second match point.
The victory nets Evans around £60,000 - almost half his career earnings so far - and, perhaps even more importantly, 90 ranking points.
Tomic has long been a frustrating talent, and he can probably empathise with Evans' previous reluctance to commit himself to tennis.
It has been a difficult year for the Australian off the court, with his father, who is his coach, barred from tournaments after being charged with assaulting Tomic's former hitting partner in Madrid, a charge he denies.
Tomic was left baffled by his own passivity during the match and, in his characteristically nonchalant way, Evans summed up his performance as "a decent effort".
He said: "Especially the first set wasn't great, was it? It was nice to come back and level it off in the second after being a break down.
"It wasn't nerves. I was pretty relaxed. He just played so slow, so strange, that I basically did what he did. I wasn't very good at it, was I?
"That's probably the best I've had to fight back. In Davis Cup I've always been pretty much up when I've won the matches. So everyone and anyone after going down a set 6-1 and 2-1 down, they think I'm done and dusted.
"That was pleasing I could find some belief inside and come back and find my game, because it wasn't there. I looked at the clock, I think it was 34 minutes, I was a set and a break down. It was looking like the airport for me."
Evans also refused to be too impressed by the way he played in the tie-break, saying: "He gave me a lot of opportunities to play. He made me look pretty good in the tie-break. He was just pushing the ball into the middle of the court."
The 23-year-old was more concerned by the ribbing he will get from his friends for a medical timeout he took at the end of the third set to have his nipples taped.
"I don't know what it was," he said. "It was just agony. The stick I'm going to get back home is devastating."
Next up for Evans is 19th seed Tommy Robredo while victory there would more than likely set up a fourth-round match against Roger Federer, with whom he practised on Wednesday.