The colourful Russian stumbled home 7-5, 6-2, 7-6 (2) on a hot Margaret Court Arena and will meet French qualifier Quentin Halys in round two.
But it was a less-than-convincing performance from the 29-year-old, who was twice broken serving for the match.
At least he was on his best behaviour, unlike last year when Medvedev was fined for mangling his racquet and a net camera in an epic temper tantrum at the same stage.
"Today was not easy. I mean, first match, Grand Slam," he said.
"Happy to win in straight sets, even if some of them were kind of up and down, but the conditions felt slow, so we were both breaking each other's serve a lot.
"The most important is to win. I'm playing better (than last year) and looking forward to this Australian Open."
The former world number one, now ranked 12, warmed up for another crack at the Melbourne Park title by winning the Brisbane International.
Medvedev fired a forehand winner down the line to break the 79th-ranked De Jong immediately and looked set to steam through the first set. But his opponent had other ideas, converting his second break point at 1-2 to haul himself back into contention.
Neither player could hold serve, with three more service breaks before Medvedev finally held to take the set after 58 minutes.
He woke up to power through the next set in 39 minutes, converting five of six break points and, with De Jong wilting, served for the match at 5-4 in the third.
But the Russian wobbled, double-faulting to give De Jong two break points, which he grabbed.
Medvedev broke straight back, again failing to serve out, but found another gear in the tiebreak to race home.
Medvedev, the 2021 US Open winner, has reached three of the last five finals in Melbourne. He was outplayed by Novak Djokovic in 2021 before a heart-wrenching defeat to Rafael Nadal a year later. He imploded against Jannik Sinner in 2024, crashing in five sets after being two up.
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