Buttler's 110 not out rescued England from the brink of defeat as they beat Australia by one wicket in the fifth one-day international at Old Trafford on Sunday to complete a 5-0 whitewash of the reigning world champions.
England, the world's top-ranked ODI side, are the tournament hosts for the 2019 World Cup.
But they have never lifted the men's version of cricket's premier one-day trophy and haven't won a knockout match at the tournament since making the last of their three losing appearances in the final back in 1992.
They also failed to get out of the group stage at the most recent edition in 2015.
"I look at the England side and Buttler is the one," Vaughan told BBC Radio's Test Match Special.
"Teams that win trophies have X-factor cricketers. He's right up there," he added.
"I've got everything crossed that he doesn't pick up an injury.
"If he's fit next year, they've got the best chance they have ever had," insisted the former Yorkshire batsman, a veteran of 82 Tests and 86 ODIs from 1999-2008.
England were on the verge of losing on Sunday as they slumped to 114 for chasing chasing just 206 for victory.
- 'Reads the game' -
But Buttler, assessing the match situation expertly, adjusted his normal policy of all-out aggression to score his slowest ODI hundred -- off 117 balls.
With Adil Rashid he added 81 for the ninth wicket before last man Jake Ball provided enough support as Buttler saw England to victory with nine balls to spare.
"What he provides to the team is that calmness," said Vaughan of Buttler. "Whenever he is out there in the middle, he reads the game better than most.
"He knows and the team know that the opposition are scared of him more than most."
England have made huge strides in 50-over cricket their miserable showing at the last World Cup in Australia and New Zealand, with this series seeing them set a new all-time men's ODI record total of 481 for six in Nottingham.
But Vaughan said the experience of winning a game where they were all but beaten on Sunday would be a bigger boost to England's self-confidence.
"Forget the 481 at Trent Bridge and the other hammerings -- this game is one England will take more from," Vaughan said.
"For them to get over the line today -- in a real close game after Australia were favourites -- this means more."
Meanwhile, Buttler tried to put hs match-winning effort into context by saying: "Everything is about building towards the World Cup but you've got to play cricket at the same time.
"We know that further down the line, with the World Cup, it's not about winning 5-0; it's about winning one-off games.
"Plucking today from nowhere shows that we've got that in us."
England came into this series on the back of a shock six-run defeat by Scotland but skipper Eoin Morgan said: ""We've progressed a lot and learnt a lot.
"We didn't start as well as we would have liked but to win 5-0 is pretty special."
The 2019 World Cup runs from May 30 to July 14.
First Published: June 25, 2018, 5:37 PM IST