Jordan Thompson recorded the quickest fifty in the history of the Vitality Blast finals as he posted the landmark score in just 17 balls.
Earlier in the match, Tom Kohler-Cadmore produced 66 off 44 deliveries to help the White Rose to what seemed a daunting 204 for seven.
Despite the tough task ahead of them, Lancashire got to work and chased down the total with six wickets and eight balls to spare.
That was largely thanks to 75 off 51 balls from Jennings who, fresh from his triple ton in the County Championship, turned on the style at Edgbaston.
Both group games between the two rival counties were decided on the last ball, but there was no dramatic finale on this occasion, with Vilas - who scored an unbeaten 63 from 36 balls - making sure his side eased to victory.
Yorkshire head coach Ottis Gibson lamented his side's bowling, saying afterwards: "To get 200 was a great effort and Jordan played exceptionally well, but basically we reserved our worst bowling performance of the season for the semi-final and that's why we lost.
"When the ball starts disappearing to all parts, it's difficult to get back in the game, you need a spark at some point. With defeat comes disappointment but you've got to be measured as well, there's a lot of things we can take out of it."
Lancashire not only became the first team to chase down a 200-plus total on Finals Day, but they did so without Jos Buttler and Liam Livingstone.
Yorkshire were also missing three key England men in David Willey, Joe Root and Jonny Bairstow who are busy on international duty.