The tourists set West Indies an improbable victory target of 438 after declaring on 333 for seven and the home team were nine for one in reply at tea, having lost Kraigg Brathwaite for five.
Ballance made amends for his miserable World Cup in Australia and New Zealand earlier this year by compiling a painstaking 122 in 250 balls.
The left-hander fist-pumped the air in delight and waved his bat to the crowd after going to three figures with a straight four off spinner Sulieman Benn.
Ballance was given good support by Jos Buttler (59 not out) Joe Root (59) and Ben Stokes (35) as England made the West Indian bowlers toil.
Captain Alastair Cook declared when Darren Bravo took a steepling catch on the mid-wicket boundary to remove Chris Jordan for 13.
Stuart Broad then struck an early blow as Brathwaite fended a hostile bouncer straight to Root at short leg on five.
Broad also hit Bravo on the point of his shoulder with another bumper just before tea.
Original source: Ballance ton lifts England victory hopes