England 277 and 325 for 4 (Root 111*, Stokes 29*) lead West Indies 154 (Campbell 41, Wood 5-41, Moeen 4-36) by 448 runs
Scorecard and ball-by-ball details
If spectators at the Darren Sammy National Cricket Stadium thought they could hear the refrain, "if only" emanating from England's dressing-room, they may not have been mistaken.
If only this match was not a dead rubber, a commanding day with the bat might count for much more than the tourists' pride. If only Joe Root's century had come in Barbados or Antigua, West Indies might not hold an unassailable 2-0 series lead. If only Joe Denly had converted his maiden half-century into a ton, he might have gone a long way towards locking down an Ashes berth after playing just two Tests.
But, with England holding a 448-run lead to put themselves on track for a consolation win and with Root playing himself into form in his final innings of an otherwise lean series, incremental gains were the order of the third day in St Lucia.
Root found his touch to reach 111 not out after his scores of 4 and 22 in Barbados (which saw his average drop below 50 for the first time since 2014) were followed by knocks of 7, 7, and 15. He gritted his teeth through a difficult period against the new ball late the day and was richly rewarded, closing his eyes and punching the air after he brought up his 16th Test hundred with a four thumped down the ground off Alzarri Joseph.
He put on a century stand with Jos Buttler, who scored back-to-back fifties for the match, racking up a second-innings 56 off 115 balls before he was bowled by a pearler from Kemar Roach that went straight through the batsman, who couldn't help but offer a look of admiration.
Denly, playing just his fourth Test innings, capitalised after being dropped by Shimron Hetmyer at third slip off the bowling of a livid Shannon Gabriel when he was on 12 to deliver an otherwise composed 69 - until his dismissal midway through the second session.
Had Denly managed a ton in England's penultimate Test before hosting Australia from August 1, he would have well and truly staked his claim for an Ashes berth. But his dismissal, caught behind off a bottom edge by Shane Dowrich while attempting to cut was welcome reward for a hard-working Gabriel and left England's summer selections as uncertain as ever ahead of the remaining one-off, four-day match against Ireland in July with four months worth of County Championship matches between now and then.
That said, Denly looked fluent in his more familiar position at No.3, having opened on debut in Antigua in place of Keaton Jennings, who failed to make the most of his recall in this Test.
Having resumed after lunch on 45, Denly brought up his 50 with a four, the 11th of his innings, before he was out three balls later.
Joseph snared the wicket of under-pressure Jennings with a ball that was missing everything before it jagged the thigh pad and curled behind the batsman onto leg stump. Jennings grinned ruefully after the freak end to his innings. With scores of 17, 14, 8 and 23 in this series, having been dropped in favour of Denly for the second Test, he perhaps realised that his time as an England Test batsman could be over.
West Indies played out their own "if only" dialogue after a bright start when Keemo Paul had Rory Burns (10) out to a regulation catch at square leg by Joseph on the first ball of the day to put England at 19 for 1.
If only Paul had not suffered a quadriceps injury chasing a Denly cover drive that had him prostrate on the grass just outside the boundary rope in agony, they would not have had to toil with a handy bowler down.
Paul - who had come into the side to replace suspended captain Jason Holder and claimed two wickets in England's first innings, including that of Jennings with his first ball of the match - ended up having to be stretchered away and taken to hospital for scans.
For the rest of the day he remained off the field, where West Indies were already missing Darren Bravo, also sent for scans, on a finger he injured earlier in the match.
Despite appearing to be in some discomfort with a hamstring problem in the morning session, Gabriel soldiered on to resume his verbal battle with Ben Stokes, who came to the crease late in the day and seemed to enjoy picking up the banter which started in the second Test.
Stokes shared an unbroken 71-run partnership with Root to be 29 not out at stumps.