That left England 315 runs behind West Indies' first innings 426 and still needing a further 166 to avoid the follow-on after Best had made the highest-ever score by a Test match No 11 during an extraordinary 10th wicket partnership of 143 with wicket-keeper Denesh Ramdin, who posted an unbeaten 107.
As the first two days of this match were washed out, England had to get within 150 runs, rather than 200, and reach 277 to avoid the follow-on.
But when Ravi Rampaul had Alastair Cook lbw, they were 13 for one.
Jonathan Trott then played on to West Indies captain Darren Sammy before Best's first Test in nearly three years got even better.
The fast bowler had England captain Andrew Strauss, trying to cut a ball that was too close to him, brilliantly caught by Darren Bravo at first slip.
England were now 49 for three.
But Kevin Pietersen (45 not out) and Ian Bell (20 not out) repaired the damage with an unbroken stand of 62, although Bell survived a sharp chance to short leg Adrian Barath off debutant spinner Sunil Narine.
Earlier, there was no hint of the torrent of runs to come when West Indies, having resumed on their overnight 280 for eight after losing the toss, saw Rampaul dismissed three balls into Sunday's play.
Ramdin, himself in Test exile for two years before this series, was then 63 not out.
But Best, who surpassed Zaheer Khan's 75 for India against Bangladesh at Dhaka in 2004 as the highest Test score by a No 11, was quicky into his stride.
He made England pay for their controversial decision to rest new-ball duo James Anderson and Stuart Broad, having already established an unassailable 2-0 lead in this three-match series.
'Stand-in' seamers Graham Onions and Steven Finn were driven in the style of a top-order batsman by the 30-year-old Best, whose previous highest Test score was just 27.
Indeed it was Ramdin who was almost out when, on 69, he cut hard at Finn and Pietersen failed to hold a sharp, head-high, chance at gully.
Off-spinner Graeme Swann went the same way as the pacemen, cut for two fours in successive balls by the inspired Best.
There was no stopping Best, who lofted Tim Bresnan, now England's senior seamer, over mid-on for four.
A single off Bresnan saw Best -- only called up to this tour as a replacement for injured fast bowler Shannon Gabriel -- complete a 44 ball-fifty.
Ramdin's single off Bresnan, after which he nearly hit the bowler's head as he waved his bat in celebration, took him to a hundred in 160 balls with nine boundaries.
Ramdin, who made 166 against England at Bridgetown three years ago, then produced a piece of paper from his pocket with "Yea Viv, talk nah" written on it, after West Indies great Vivian Richards had criticised him for failing to deliver on his promise after the tourists's nine-wicket second Test loss.
Best uppercut Bresnan over the slips for yet another boundary to surpass Zaheer's record and then drove him for a stunning straight six.
Few would have begrudged Best a hundred, but he fell just short, skying an Onions slower-ball to Strauss at first slip as the home skipper equalled the England Test record of 120 catches by an outfielder held by Colin Cowdrey and Ian Botham.
Best faced just 112 balls with a six and 14 fours.
His partnership of 143 with Ramdin was a West Indies record for the 10th wicket in Tests, overtaking the 106 shared by Carl Hooper and Courtney Walsh against Pakistan at St John's in 1993.
