The Premier League side defeated the Serie A champions 6-5 on penalties after a 1-1 draw in the pre-season International Champions Cup in San Francisco.
And Stones, who moved to Goodison Park from Barnsley in January, stole the show in the decisive shoot-out when he converted a cheeky dinked penalty after Andrea Pirlo had sent his kick wide for Juventus.
| MARTINEZ ON WIN OVER JUVE
|20/1||Everton are 20/1 with William Hill to finish in the top four
"I knew he was going to do it because the last three he has taken in training he has done that. The question was could he do it after Andrea Pirlo and at his age," the Spaniard told the club's official website.
"It was incredible and I thought it was an example of his performance. He was composed throughout and it was a very useful game for himself and [he could be] a very important 'new' player for us going forward."
Stones also helped to nullify the Antonio Conte's dangerous new-look attack of Carlos Tevez and Fernando Llorente during the game, and will now get the opportunity to pit himself against either LA Galaxy or Real Madrid in the next round of the tournament.
The friendly match proved a good test in the Everton's build-up to the new Premier League season and Martinez was pleased with the outing.
"It was really, really useful," he added. "The effort from the players and the understanding to go toe-to-toe with such a good side was a really good exercise."