West Indies began the final day trailing by 30 runs on 83 for three but hopeful of salvaging a draw.
However, they suffered an early setback with Chris Gayle edging Matthew Hoggard behind in the fifth over of the morning.
For the rest of the session all-rounder Dwayne Bravo was a model of restraint, resisting his attacking instincts to keep the dependable Shivnarine Chanderpaul company for 13 overs and taking West Indies into the lead.
Bravo, though, took leave of his senses immediately after the interval and instead of the determined, disciplined batsman who had battled for 67 minutes before lunch, he was transformed into a one-day slogger.
Harmison was hit for three boundaries in two overs and Vaughan immediately introduced Panesar at the other end to inevitable consequences — Bravo hit him over mid-on for four and was caught at mid-off attempting the same shot off the next delivery.
Chanderpaul had every reason to be furious with Bravo for his irresponsible performance after lunch, which prompted a mini-collapse with Panesar claiming three wickets in 24 balls to leave any hopes of salvaging a draw looking almost impossible.
Marlon Samuels was caught at slip and Denesh Ramdin bowled with a fiercely-turning delivery to leave Chanderpaul battling with the tail once again.
Harmison charged in from the other end with renewed venom and Daren Powell looped the ball to mid-off.
Fidel Edwards’ stumps were also demolished by Harmison, but it was Panesar who finally broke the resistance of Chanderpaul, on 70.
Chasing a modest victory target, England lost Alastair Cook early when he edged Powell to slip and Andrew Strauss lost his off stump to an inswinger from Powell. That, though, only set the stage for Vaughan and Kevin Pietersen to forge a 76-run stand off only 68 balls, which was only broken with five runs required when Pietersen edged to slip.
Local hero Paul Collingwood hit the winning runs to end the one-sided series.
Vaughan himself finished unbeaten on 48 after announcing yesterday he would give up the one-day captaincy.
Vaughan said: “I really believe a new captain at the helm in that form of the game is what the team needs.
“We won 3-0 and now we can look forward to the remainder of the summer. We have a great chance of winning the one-day series.”
Monty Panesar was named England’s man of the series, largely thanks to his 10 wickets at Old Trafford.
The Northamptonshire spinner said, however, he does not believe he is guaranteed his England place in either format of the game.
“I’ve still got a long way to go for that,” he said. “It’s been an unbelievable series, the four Tests and taking 23 wickets. I feel quite lucky with the way things have gone. We’re pleased with our performances.”
West Indies captain Daren Ganga admitted his side had not performed well enough over the series: “There was a lack of consistency that we probably wanted in this series and unfortunately we just fell short.”