At the close of Sunday's fourth day, the tourists were seven without loss in their second innings, needing a further 394 on Monday's final day to reach their victory target of 401.
Chris Gayle, struck a painful blow in the groin by Stephen Harmison, and Daren Ganga survived the two overs before the close.
Pietersen's seventh Test century was the centrepiece of England's second innings 284 for eight declared which gave them a lead of exactly 400.
Corey Collymore dismissed all of the top three on his way to three for 58 and part-time off-spinner Gayle took three for 66 as England went in search of quick runs.
Pietersen, together with Paul Collingwood, one of four England century makers in their first innings 553 for five declared, he put on 102 after Corey Collymore had taken three wickets.
Matt Prior, who earlier in this match became the first England wicket-keeper to score a century on Test debut with a rapid 126 not out, maintained that form with 21 in nine balls including two sixes off medium-pacer Dwayne Bravo.
The batsmen built on the good work of left-arm spinner Monty Panesar whose haul of six for 129 gave England a healthy first innings lead of 116.
At tea on the fourth day England were 105 for two, a lead of 221, with Alastair Cook 52 not out after his first innings 105, the 22-year-old Essex opener's fifth hundred in his 15 Tests, and Pietersen unbeaten on 21.
England endured a lull, going 104 balls without a boundary until Pietersen drove Collymore, straight back over his head.
After Cook was caught behind for a patient 65, Pietersen upped his tempo by scoring four fours - the best a commanding pull - in Collymore's 15th over which cost 18 runs.
England knew they had to score rapidly if they were to give their depleted attack the best possible chance of bowling West Indies out for a second time.
Pietersen, 26, took up the charge with a resounding front-foot cover-driven four off Bravo before driving Daren Powell down the ground and into the Pavilion fence.
One ball after Collingwood had been dropped on 29 at long leg by Powell off Bravo, Pietersen went to a hundred. The South Africa-born batsman's second fifty had come in a mere 39 balls, his 100 stand with Collingwood up in 94.
After Collingwood holed out, Ian Bell - not suited to bashing quick runs, came and went quickly.
Pietersen was then plumb lbw trying to reverse-sweep occasional off-spinner Chris Gayle, having hit 12 fours in his 138 ball innings. And three deliveries later 264 for six became 264 for seven when Gayle had Liam Plunkett stumped for nought.
Panesar's return was the fourth time in his 14 Tests that the 25-year-old had taken five or more wickets in an innings.
And with England a pace bowler short as Matthew Hoggard (thigh) remained off the field and in the absence of the already-injured Andrew Flintoff, they needed Panesar's wickets and control.
West Indies, eventually all out for 437, resumed Sunday on 363 for seven, 190 runs behind, but having survived the follow-on with senior batsman Shivnarine Chanderpaul 63 not out.
Chanderpaul, who'd shared stands of 92 with Bravo (56) and 83 with Ramdin (60) on Saturday, succumbed to Panesar's fourth ball Sunday when on 74, the left-hander was hit on the back leg by a ball that turned out of a footmark.
Chanderpaul, who in the Lord's Test three years ago scored 128 not out and 97 not out, had batted for over four hours and faced 193 balls with nine fours.
Panesar subsequently became only the fifth bowler in all and first spinner to claim five lbws in a Test innings when he snared last man Collymore.
Australia's Terry Alderman, West Indies' Curtly Ambrose, Pakistan's Mohammad Zahid and England's Richard Johnson had all previously achieved the feat.