Both men cleared five metres 36 times in 30 minutes with 2012 Olympic champ Lavillenie making his last clearance just before his Swedish rival.
A three-minute jump-off for the gold was suggested, but Lavillenie said, "I'm done, I don't want to take any risks."
World record holder Duplantis was keen to continue and vaulted once more before holding up a score of 37 at the end.
Two-time reigning world champion Sam Kendricks was third after making 26 successful clearances.
"We can say that I am the first winner and Mondo is the second winner." - Renaud Lavillenie
The first pole vault event of its kind
It was former world record holder Lavillenie who had the idea of going up against his friends and rivals at home while they are affected by measures to prevent the spread of COVID-19.
The Frenchman has been training for weeks at home in Clermont-Ferrand with his brother Valentin, who reached the final of the pole vault at last year's World Championships in Doha, occasionally providing commentary.
He reached out to his buddies across the Atlantic - Duplantis in Lafayette, Louisiana and Kendricks in Oxford, Mississippi - and the event was born.
With lockdown measures making it impossible to calibrate heights exactly, the three decided on a speed challenge with the winner clearing five metres the most times in the space of 30 minutes split into two sessions.
Lavillenie thought one jump per minute might be a good benchmark with Duplantis - who was 'competing' in his parents' garden where he started pole vaulting at the age of four - saying he would "come out attacking and try to hang on the end".
Duplantis lived up to his pledge by averaging one clearance every 45 seconds, marginally quicker than Lavillenie, with Kendrick opting to conserve his energy by taking over a minute between each attempt.
The American-born Swede lost his advantage briefly due to an aborted attempt, but Lavillenie also made a failure as Duplantis reached 18 at halfway - one ahead of the Frenchman - with Kendricks back on 13.
Despite saying admitting he was "gassed" at the midway point, Duplantis kept up his strong pace but Lavillenie was determined to stay with him.
In the last two minutes, Lavillenie managed to go into the lead for the first time but there was very little in it.
They both finished on 36 and, despite Duplantis wanting to carry on, a tie was the eventual outcome.
Stefanidi leads social media reaction
Plenty of athletes tuned in to watch the action unfold on the World Athletics live stream.
Rio 2016 women's pole vault champion Katerina Stefanidi said on Twitter at the midway point "We need to raise the bar for the second part!!"
And when European Athletics council member Marton Gyulai suggested a women's version with Sandi Morris, Jennifer Suhr, Holly Bradshaw and Angelica Bengtsson, the Greek said she would love to.
The event certainly captured attention worldwide with Sydney 2000 400m bronze medallist Katharine Merry calling for more events in the future.
And while Kendrick was back in third place, USA Track and Field had the last laugh.