The West Indies were bowled out for 295 in the afternoon – surrendering a 104-run deficit – but grabbed three early wickets with the new ball to force their way into contention.
Further inroads would have left England approaching the penultimate day with apprehension, but Ballance and Root shared an unbroken stand of 64 to leave their side 116 for three at the close.
On an entertaining, and often evenly matched day at the Sir Vivian Richards Stadium, James Tredwell’s four wickets for 47 runs and Jermaine Blackwood’s maiden Test century were the individual highlights.
James Anderson took one more wicket to move to within just one of Sir Ian Botham’s record 383 Test scalps – but he was peripheral at times.
For Tredwell it was a good response to the news England were flying the fit-again Moeen Ali out ahead before the second Test.
Moeen’s summons is an eminently sensible one given his success against India last summer, but Tredwell’s display of nagging accuracy made its own case.
Blackwood’s unbeaten 112 was an idiosyncratic effort, built as much on grim determination as free-spirited blasts over extra-cover.
Despite the comfort of a three-figure lead England openers Jonathan Trott and Alastair Cook failed for the second time in the match, although it would be churlish to deny Jerome Taylor’s role in their downfall.
He sent down a fine new ball spell, beating Trott’s outside edge in his first over and clipping it with a full, swinging delivery at the end of his third.
Trott had at least moved off a pair by then but a return of six runs in his last four innings on tour must be a major cause for concern.
Taylor was well in the groove though and needed just four more balls to see off Cook.
The England skipper had seemed sure-footed on his way to 13 but was tempted to follow a delivery outside off stump and squirted a waist-high catch to gully.
Bell, on the back of a fine 143, had a quite torrid time.
He played and missed at good balls from Taylor and Kemar Roach, while Jason Holder worried Ballance with swing.
Tension must have played its part when Bell was run out for 11, sent back by his partner having scampered halfway down the track.
But the final hour was England’s – Ballance finding his feet after drinks with three boundaries in 11 balls and Root scoring confidently off the spin of Sulieman Benn and Marlon Samuels.
By the time stumps were taken the pair were timing the ball nicely and sitting on a vital 64-run stand.
England began the day seeking to prise apart the pairing of Blackwood and Shivnarine Chanderpaul – but it was not until the 13th over that they made the breakthrough, Anderson, Stuart Broad and Ben Stokes all having tried and failed.
Tredwell got the wicket, sucker-punching Chanderpaul shortly after he had replaced Mahela Jayawardene as the seventh highest run-scorer in Test cricket.
Having made 46 in 139 balls, the 40-year-old ignored a stacked offside field when Tredwell floated one up and picked out one of two catchers at short cover.
Holder and Roach would later fall to Tredwell as he created pressure through patience and accuracy.
Blackwood, having started the day on 30, would end the innings unbeaten. He gave chances – Tredwell grassing a tough one at slip and Jos Buttler reaching an awkward fend on the bounce – but showed real grit in his 220-ball stay.
He traded blows with Stokes and Broad in particular, taking the bruises where necessary but producing thrilling counter-punches too.
Broad was also impressive, turning in one of his more hostile spells in recent memory. He found the new ball to his liking and worked hard for his only success of the day, Denesh Ramdin gloving one away from his ribcage.
The West Indian tail subsided quickly at the end, with Jerome Taylor run out and Benn turning Anderson to short leg.
That wicket will hardly go down as one for his scrapbook – but with history beckoning for the 32-year-old, every one counts.
With the game finely balanced he will surely fancy his chances of succeeding Botham before leaving Antigua.