Vaughan, who had not played a Test since December 2005 because of a career-threatening knee injury, scored 103 in England's first innings 570 for seven declared and then saw his bowlers get the job done after West Indies followed on.
West Indies were bowled out for 146 and then 141 to slump to their heaviest Test defeat of all time.
"It's been a great week," Vaughan, who joined Peter May as the most successful England captain, told reporters. "I couldn't really have asked for much more. I'm pleased to go 1-0 up.
"With the rain that was around we started to wonder whether it was going to be one of those games that cost us but in the end I'm delighted.
"I thought we played to a very good standard and were ruthless for most of the match," added Vaughan, who preferred to concentrate on his own team's success rather than the deficiencies of England's opponents.
Vaughan had special praise for his former Yorkshire team mate Ryan Sidebottom, who claimed eight for 86 in the match after an impressive display of left-arm swing bowling in helpful, overcast conditions.
"Ryan was exceptional from his first ball," Vaughan said.
"He certainly didn't swing the ball like that when he was at Yorkshire. I don't know what they have been doing with him at Notts," Vaughan added with a smile, following Sidebottom's switch to Nottinghamshire in 2004.
Vaughany vouch for Harmi: Vaughan was hopeful Old Trafford would again inspire Stephen Harmison after the fast bowler failed to fire for much of the side's emphatic victory at Headingley.
Harmison was reduced to the status of a supporting act in a match where left-arm quick Ryan Sidebottom called the shots.
But for much of the game both Harmison and county colleague Liam Plunkett were wayward, Harmison in particular testing the agility of wicket-keeper Matthew Prior with several legside deliveries.
It was a concern for England, otherwise utterly dominant, after Harmison had been off-target in the drawn series opener at Lord's following his lacklustre display during their 5-0 Ashes thrashing in Australia.
But Vaughan, who marked his return to Test cricket after 18 months out injured with 103 in England's 570 for seven declared where Kevin Pietersen's Test-best 226 was the centrepiece, said Harmison would be a different proposition at Old Trafford, Manchester.
Last year at the Manchester venue, on a lively pitch, Harmison took 11 for 76, including a first innings haul of six for 19, as England overwhelmed Pakistan by an innings and 120 runs.
"Steve has openly admitted he hasn't had the best six months. Old Trafford has always been a great ground for him, he'll be looking to reproduce the performance he showed against Pakistan last year," Vaughan also told reporters on Monday after his commanding return to Test cricket on his Yorkshire home ground.
There were signs of the Harmison of old as West Indies lost their last three wickets for no runs in eight balls.
"I thought then Steve Harmison was back to what we know he can be," Vaughan said. "That was bowling 90mph, getting bounce off a good length, and putting batsmen under a lot of pressure when the wicket wasn't swinging."