Yorkshire, inserted, slumped to 28-3 inside 10 overs.
Without injured in-form opener Imam-Ul-Haq (hip), they lost Adam Lyth bowled by a beauty from Ball, Will Luxton run out next ball and James Wharton caught behind one-handed going low to his right by James Rew off Ben Green.
Luxton misjudged a push to mid-off, where Josh Thomas mis-fielded before recovering to throw the non-striker’s stumps down.
Revis, who hit nine fours, held things together on the pitch used for Tuesday’s win over Lancashire, with Yorkshire compiling nothing more than a workable total.
Fin Bean, on 28, cut 18-year-old debutant seamer James Theedom to backward point with the score on 72 in the 18th over.
Revis reached a 49-ball 50 shortly before Yorkshire reached the halfway mark in their innings at 115-4.
He found an ally in fellow all-rounder George Hill. They calmly shared a recovery fifth-wicket partnership of 102.
Yorkshire then lost four quick wickets, including Revis and Hill caught pulling, as the score fell from 174-5 in the 36th over to 204-8 in the 42nd. Green’s second wicket accounted for Revis, 34-year-old Ball’s second was Hill for 41.
Tom Lammonby’s left-arm seam also claimed two wickets in that period.
Dan Moriarty heaved the only two sixes of Yorkshire’s innings in a career-best 30 before holing out to cover as Ball struck twice in the 49th over to wrap things up.
Opener Vaughan, in his first competitive senior career appearance against his birth county, steered Somerset’s stress-free chase.
Lammonby was well caught at deep gully by Lyth off Hill en-route to 48-1 after 10 overs before 19-year-old Vaughan shared a second-wicket partnership of 70 with Lewis Goldsworthy (30).
Vaughan reached his fifty off 65 balls but Goldsworthy fell at 111-2 in the 25th over when he top-edged a pull at Revis to long-leg.
Vaughan continued on unflustered, sharing 64 with his captain James Rew. But he was bowled looking to go over the top against Dom Bess’s off-spin. Still, at 175-3 in the 38th over, Somerset were in a strong position.
James Rew finished unbeaten on 53 off 62 balls, while brother Thomas also contributed 31.
Match report supplied by ECB Reporters Network, supported by Rothesay