Jimmy left stranded on 499 wickets
Anderson appeared destined to reach the landmark after he snaffled the first two wickets of the day.
Starting the day on 497 Test victims, Anderson soon moved to 499 when he had both Kraigg Braithwaite (10) and Kyle Hope caught behind by Jonny Bairstow.
At that stage, the West Indies were 22-2, but despite bowling beautifully, Anderson was unable to take a further wicket as Stokes and Toby Roland-Jones (2-32) ran through the rest of the card.
The Lancashire paceman is currently sixth on the list of all-time leading wicket-takers.
He is now just 20 wickets behind West Indian Courtney Walsh's haul, although he is still some way short of Australian Glenn McGrath's mark of 563, who is fourth on the list.
Sri Lanka's Murali Muralitharan is the highest wicket taker with 800 wickets, ahead of Australian Shane Warne (708) and India's Anil Kumble (619).
Anderson, who attended St Theodore's RC High School, began his career with Burnley in the Lancashire League.
After breaking into the Lancashire team and taking the wickets of ex-England batsmen Nasser Hussain and Mark Ramprakash as a teenager, he was called up by England for their one-day squad in Australia nearly 15 years ago.
The following summer, he made his Test debut at Lord's - taking 5-73 against Zimbabwe.
He has since gone on to become one of the greats of the game - helping England to Ashes success both at home and abroad.
In April 2015, while playing against the West Indies, he became his country's all-time leading wicket-taker when he surpassed Sir Ian Botham's long-held record of 383 wickets.