The pair had been forced off court by the fading light on Monday night at 5-5 in the deciding set after three hours and 55 minutes of power tennis in a tremendous atmosphere on Roland Garros' bullring court.
With the French Open now the only grand slam tournament not to use a deciding-set tie-break, there was the prospect of a lengthy denouement, but instead Edmund broke the Chardy serve at the first time of asking.
Edmund said: "Best of five was a marathon, but this was a sprint today, and I just went for it. It's tricky, especially emotionally. You're in the match and then you've got to switch off.
"I got out of here 11pm last night, and arrived at 9am today. It's all part of the game. I think that is the longest match I've played. It was really good for me to come through that test."
The result was a timely boost for the British number one, who snapped a five-match losing streak dating back to early April.
He faces tricky Uruguayan Pablo Cuevas next as he bids to reach the third round here for a third successive year.
There was significantly less good news, though, for British number two Cameron Norrie, who fell to a humiliating defeat by French qualifier Elliot Benchetrit.
Norrie, who has climbed into the world's top 50 this year, looked to have a kind draw against the world number 273 but, while Benchetrit was inspired in front of his home crowd, the British number two was off colour from the start.
A break for Benchetrit in the third game set the tone, and Norrie lost the second set to love in less than 20 minutes before eventually going out 6-3 6-0 6-2 in an hour and 24 minutes.
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