Prior, 25, was one of four England centurions in the innings with Alastair Cook (105), Paul Collingwood (111) and Ian Bell (109 not out) also reaching three figures.
It was the first time since 1938 that four England batsmen had all scored centuries in the same Test innings when Charlie Barnett (126), Len Hutton (100), Eddie Paynter (216 not out) and Denis Compton (102) contributed to a total of 658 for eight declared against Australia at Trent Bridge.
Prior, who gave Bell a 56-run head start, beat his team-mate to three figures in a rapid 105 balls with 16 fours.
Bell reached the landmark in 180 balls, the batsman's sixth Test century. When bad light forced an early close, the duo had put on an unbroken 190 in 212 balls for the sixth wicket.
Four West Indies bowlers conceded over 100 runs each, Jerome Taylor the most expensive with one for 114 from 24 overs.
Collingwood, twice missed in the 30s and lucky to survive an lbw appeal, received good support from Bell, in a fifth-wicket stand of 144.
England, against a right-arm seam attack lacking variety and genuine pace - a worrying sin for West Indies at the outset of a four-Test series - resumed after tea well-placed at 372 for five with Bell 59 not out and Prior unbeaten on five.
Prior, who played under new England coach Peter Moores at Sussex, had got off the mark before tea with a four through mid-wicket off Dwayne Bravo.
And he maintained his tempo on the way to a 55-ball fifty, the 25-year-old reaching the landmark with an emphatic hooked four off Daren Powell.
West Indies captain Ramnaresh Sarwan, an occasional leg-break bowler, brought himself on with England 446 for five off 129 overs.
But his first two balls, both short and wide, were gleefully seized on by Prior for consecutive fours.
England were now well on the way to building a total even a side featuring now retired former West Indies captain and batting great Brian Lara would be hard-pressed to overhaul.
Off-spinner Chris Gayle was then driven for four by the South Africa-born Prior, who came to England as an 11-year-old. Prior drew level with Bell on 95 when he pulled a long hop from Gayle for four.
Collingwood's century was his fourth in 21 Tests and second at Lord's after his 186 against Pakistan last year where Bell too also made a hundred.
But medium-pacer Dwayne Bravo made the breakthrough by bowling Collingwood to leave England 363 for five.
England, who began Friday on 200 for three after losing the toss, had enjoyed the better of Thursday's play against a West Indies side now in a lowly eighth place in the world Test rankings.
Cook was 102 not out and Collingwood unbeaten on 21 after the tourists, not helped by a lack of match practice that meant they hadn't bowled any 'live' overs since arriving in England, had failed to exploit helpful cloud and pitch conditions fully.
But the bowlers now had the benefit of 56 overs behind them and were the better for it. Taylor was unlucky when Durham's Collingwood, on 31, drove loosely only for Daren Ganga at gully to drop the two-handed catch.
Soon afterwards Taylor had an lbw appeal against Collingwood, now on 32 and playing no stroke outside off-stump, rejected by Pakistan umpire Asad Rauf.
First change Corey Collymore should have had Collingwood out for 36 when a top-edged hook lobbed towards backward square leg where Taylor dropped the catch.
However, Cook was out to the first chance he offered when a square cut off Taylor was caught at backward point by Bravo.
The 22-year-old left-hander batted for just short of five hours and faced 196 balls with nine boundaries in what was his fifth hundred in 15 Tests.