Bashir took 5-41 as the West Indies collapsed to 143 all out on the fourth evening, with England triumphing by 241 runs to take an unassailable 2-0 lead in a three-match campaign.
It was Bashir's third five-wicket haul in just five Tests but first in England after he twice achieved the feat on spin-friendly Indian pitches earlier this year.
His latest exploits were all the more impressive given Bashir did not bowl a single ball and was out for a duck during England's innings and 114-run thrashing of the West Indies in the first Test at Lord's.
Bashir removed Kirk McKenzie, Kavem Hodge and Alick Athanaze -- all top-order batsmen -- in quick succession before bowling Jason Holder and last man Shamar Joseph as West Indies, set 385 to win, slumped to 143 all out.
'Pretty cool'
"I think what Bash has done today is to show the world what he can do," said England captain Stokes.
"That wicket hardly offered anything for a spinner throughout the whole Test match and look at what he was able to do today.
"The way in which he can change his pace, produce over-spin and under-spin...I think he showed his full bag of tricks. He's got so much talent and the ceiling is so, so high. He's got an unbelievable desire and a will to get better and learn."
Stokes added: "It's really good for a young guy to come out and put in a performance that wins England a Test match, it's pretty cool for him."
For all his success in India, rising star Bashir was unable to break into the Somerset side at the start of the season after the side opted for a more experienced England spinner in Jack Leach.
That led Bashir to go on loan to Worcestershire last month, but England kept faith with him all the same.
"The decisions we make are all based around not only how far we think their talent can take them, but whether we think they're good enough for international cricket straight away," explained Stokes.
"I don't want to sound like it's an 'I told you so' kind of thing but it sort of is."
