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Hewitt had been due to face French Open finalist Roger Federer in the first-round match - a repeat of last year's final - but the Swiss star's withdrawal on Monday saw Mayer promoted to the main draw.
Hewitt eased to a 6-2, 6-3 win and the former world No 1 needed just over an hour, blasting down six aces - four of which came in the first set - and was rarely troubled by the Argentinian, ranked 206th in the world.
"I don't feel too bad, I had no expectations going out there," said Hewitt after the win which will see him play Italy's Andreas Seppi in the second round.
"You have to adjust to the climate and the conditions - obviously the practise courts here in Halle are very different to the centre court.
"My body feels pretty good - after Paris I went to London for a few days to practise on grass."
Having been denied the chance to face world No 3 Federer, Hewitt said he anticipated the Swiss star's withdrawal from Halle, especially with Wimbledon starting in ten days.
"Seeing that I was due to play Roger Federer in the first round did not bother me, I didn't worry about the draw," said Hewitt who is making his first appearance since January's Australian Open after an ankle injury.
"I am focusing on my fitness and my matches.
"This time of the year is very difficult since we have two majors so close together.
"With Roger having played two tough weeks in Paris, I saw a small chance that he might pull out."
Hewitt is making his comeback and after undergoing ankle surgery, on the back of two hip operations in the last two years, but the 30-year-old says he is glad he has taken his time.
And he had some advice for Germany's Tommy Haas who is also making his comeback from injury.
"I have to say that you cannot hurry things up," said Hewitt after Haas lost over three-sets to Seppi on Tuesday.
"I have been out of the game for over three months and I feel it tough to re-adjust, but Tommy has been out for over a year.
"I absolutely think that Tommy has a chance to come back, but he has to concentrate on getting back into points and matches."
Hewitt says he is looking to rediscover his game and ignores his current ranking of 78th in the world.
"I could not care less about points, ranking is not important to me," he said.
"I have to pick up my game again, my timing, movement, footwork - everything has to become second nature again."
