Evans had battled for three and a half hours to get past Facundo Bagnis in extreme heat in the first round but needed less than two hours to wrap up a 6-4, 6-4, 6-1 victory over 35-year-old Chardy in much cooler conditions.
The veteran Frenchman was incensed by an incident in the seventh game of the first set when, facing break point, a ball fell out of his pocket during play, which would normally cause the point to be replayed.
But German umpire Miriam Bley did not notice until a split second after Chardy netted and awarded the point to Evans.
Chardy argued his case at length and the supervisor was called to court but the decision remained the same.
He did not hold back afterwards, saying: "It's a big mistake from the umpire. I was angry because she should stop straightaway, and she says she didn't even see the ball.
"I don't know what she's doing because she doesn't call in or out, she just called the score, and if she doesn't watch the point, I don't know why she's on the chair. So I was p****d, and I was even more p****d when she didn't tell me she made the mistake."
Chardy believes umpires should face sanctions in such situations, saying: "It's what I said to her. If I miss a point, then break my racket, I will get fined. You can do a huge mistake and nothing will happen to you. So I think this is not fair."
Evans was happy to sit on his chair and wait for the situation to be resolved, and Chardy continued to voice his complaints to the umpire as the British number two wrapped up the opening set.
Evans then broke serve against to start the second before running away with the third as Chardy, playing his first tournament since the US Open in 2021 following knee surgery, tired.
Evans said of the incident: "The only part I wanted to clear up was I was just simply asking the umpire why it was a let. I didn't see any of what happened, because obviously the play was all in the other corner. I think it went on a bit too long, and it got cleared up, and then I did a good job of holding.
"I know Jeremy relatively well, so I didn't really want it to sour the match. If it was someone I didn't know so well, I'd be hoping he was getting fired up and a bit angry with the situation.
"I don't really know what to make of what happened. I don't really know who was in the right and who was in the wrong. It was just a pretty awkward situation."
Evans would like to see the rule changed, saying: "I think it's the worst rule ever. If a ball comes out of your pocket, it's your own fault."
The 32-year-old, seeded 25, has been a consistent performer at the Grand Slams over the past few years and is pleased to have made the third round again.
"I've done my job so far, win my matches relatively well," he said. "Whoever I play next will be a tough match."