Prior became the first England wicket-keeper to score a century in his debut Test with a blistering 126 not out as the hosts reached 553 for five when bad light forced an early close on the second day of the four-Test campaign.
The Sussex gloveman's century was the fourth of the innings after opener Alastair Cook (105), Paul Collingwood (111) and Ian Bell (109 not out) also reached three innings.
It was the first time four England batsmen had all scored centuries in the same Test innings for 69 years.
England have struggled to find a keeper who can contribute with both bat and gloves at Test since former captain Stewart retired four years ago.
Prior, 25, has since been mentored by Stewart and said his input had been invaluable. "Alec Stewart has been fantastic. He was the third person I called (following his England call-up) after my mum and dad.
"It's great to have someone like Alec Stewart at the end of a phone to explain things and calm me down," Prior added.
He was only the third wicket-keeper in Test history to score a century on Test debut, joining Sri Lanka's Brendon Kuruppu (201 not out against New Zealand at Colombo in 1986-87 and Romesh Kaluwitharana (132 not out against Australia) at Colombo in 1992-93 in an exclusive club.
Prior, born in Johannesburg to an English father and South African mother but who came to England as an 11-year-old, said: "It doesn't get any better than this for an Englishman on debut at Lord's. It's a fantastic feeling."
He drove confidently through the covers and pulled aggressively, reaching three figures in just 105 balls and beating Bell to three figures despite giving his team-mate as 56-run head start.
At stumps Prior, who played under new England coach Peter Moores at Sussex, had maintained his rapid tempo, having faced just 128 balls in all. Together with Bell, he'd shared an unbroken stand of 190 in 212 balls.
It all emphasised how far West Indies, once Test cricket's most feared side but now ranked eighth in the five-day game, had fallen from their 1980s and 90s heyday when fast bowlers such as the late Malcolm Marshall, Michael Holding and Curtly Ambrose used to terrorise the world's best batsmen.
And they didn't help themselves by twice dropping Collingwood in the 30s.
England's total was achieved without the injured duo of first-choice captain Michael Vaughan and all-rounder Andrew Flintoff, who could both return for the second Test at Headingley starting a week Friday.