Robson and Ballance stand firm against India
England batsman Gary Ballance (L) plays a shot during the third day's play in the first Test between England and India at Trent Bridge in Nottingham, central England on July 11, 2014 - by Andrew Yates
England were 131 for one in reply to India's first innings 457, a deficit of 326 runs, at lunch on the third day.
But they had not lost a wicket during Friday's morning session, although Robson was dropped on 43.
Both Australia-born opener Robson and Zimbabwe-born Ballance were 59 not out after they had each completed a fifty in 123 balls.
England, without a win in their last eight Tests, resumed on 43 for one after captain Alastair Cook had been bowled round his legs for five by Mohammed Shami on Thursday.
That made it 25 innings since Cook had scored the last of his England record 25 Test hundreds, with his average in that period a meagre 24.
India's total owed much to a record last-wicket stand against England of 111 between Bhuvneshwar Kumar (58) and Shami (51 not out).
England, after two days of bright sunshine, saw Robson (20 not out) and Ballance (15 not out) walk out Friday in overcast conditions that promised to assist India's seamers on a still largely docile pitch.
Robson, who in common with Ballance scored his maiden Test century during England's recent series defeat by Sri Lanka, was quickly into his stride.
He cover-drove Shami for four and next ball clipped the seamer off his legs for another boundary.
Shami gave way to the quicker and taller Ishant Sharma -- the only member of India's attack to have previously played a Test in England.
Sharma unsettled Robson with a well-directed bouncer, one of the few balls to rise sharply on a slow surface, that struck the batsman's gloves in front of his face.
Left-hander Ballance, though, clipped Sharma off his pads, cut him and turned him square again for three fours in five balls after going 63 balls without a boundary.
However, Robson had an escape when he turned left-arm spinner Ravindra Jadeja behind square only for leg-slip Virat Kohli to drop the low catch.
Ballance then late-cut debutant all-rounder Stuart Binny to the third man boundary to complete his fifty and Robson's similar shot off the medium-pacer got him to the landmark as well.