In a poor West Indies batting display, Devon Smith top scored with 26, though Runako Morton, caught behind when he had not hit the ball, was unlucky.
Sidebottom then trapped Daren Ganga and night-watchman Daren Powell lbw in the second innings, after he had Chris Gayle dropped on six by wicketkeeper Matt Prior.
Gayle finished on nine as England eyed taking a 1-0 lead in the four-match series.
West Indies were demoralised by Pietersen's innings, which surpassed Robert Key's 221 against West Indies in 2004 and trailed only Graham Gooch's 333 against India in that time.
The Hampshire batsman put on 160 with Prior in 211 balls, with Prior making 75.
England took just seven overs to progress from 500 to 550 as Plunkett scored a test best 44 not out.
Pietersen, who resumed on 130 from overnight, managed to finally better his previous test score of 158, which he had registered on three occasions, twice against Australia and once against Sri Lanka.
He said: "I was very excited to go past it. On 156, I was definitely going to have a go at something as I wasn't going to go 157, 158. Fortunately one went down to the boundary."
Some of his shots were majestic, perhaps the best one a flick through the on-side for four that split the mid-on and midwicket fielders, from a Dwayne Bravo delivery that was on off-stump.
West Indies' situation, in a match in which they have already lost captain Ramnaresh Sarwan to injury, deteriorated when a top-edged hook from Plunkett was dropped by Corey Collymore at fine leg as he juggled the ball over the boundary rope.
When Pietersen was eventually caught at deep extra cover off Bravo, he had faced 262 balls.
Only Australia's Donald Bradman scored more runs (3,194) after 25 tests than Pietersen (2,448).
Sarwan, who injured a joint in his shoulder while fielding on Friday, will bat in the second innings "only if it is absolutely necessary", team spokesman Imran Khan said.
England's Ian Bell did not take the field because of a stiff lower back.
Test cricket's second-ranked team England, who were beaten by champions Australia 5-0 in January, have not lost a test series at home to West Indies since 1988.