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.
The third Test starts at Old Trafford, Manchester on June 7.