McLaren's official reserve Vandoorne flew in from Japan on Friday, after Spaniard Fernando Alonso failed a medical, and he seized the opportunity with the double world champion remaining at the track to give him advice.
His 10th place, after starting 12th on the grid, made him the 62nd driver since the championship started in 1950 to score in his first race.
Vandoorne had already out-qualified 2009 champion Jenson Button in the other McLaren, with the Briton retiring on lap seven with a power unit failure.
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"This result was more or less what I expected," said last year's winner of the GP2 support series, who has been tipped as a big star of the future and has been racing in Japan this year to keep up to speed.
"The start was a little bit difficult. There was debris left and right, it was pretty hectic in fact, and there was a lot of fighting throughout that opening lap.
"I'm pleased that I didn't make any mistakes operationally -- I was really focussing on that side of things -- and I came away with a point, which was a nice bonus."
A single point would once have been considered failure by McLaren, the second most successful team in the sport's history in terms of wins, but they have won nothing since 2012 and last year suffered their worst season.
The signs for 2016 are already better -- it took McLaren six races before they scored a point last year as they started a new partnership with Honda -- and Button was third fastest in Friday practice.
McLaren Racing Director Eric Boullier said Vandoorne, who could also drive for McLaren in China on April 17 if Alonso fails to pass a medical before that third race of the season, had put in a "flawlessly mature" performance.
He said Button might have finished at least seventh, and possibly higher, without the problem but Vandoorne "didn't put a foot wrong".
Boullier added: "Having done such a good weekend, it's a massive boost of confidence (for him). A boost for his career. The whole weekend went trouble-free.
"We definitely didn't put any pressure on him but he did a brilliant job."
(Reporting by Alan Baldwin, editing by Ian Chadband)
