England were bundled out for 191 in the first innings with Ojha taking five for 45 while Ravichandran Ashwin took three wickets, prompting India to enforce the follow-on.
But the script changed remarkably in the second innings as skipper Alastair Cook (74 batting) and Nick Compton (34 batting) steered England to 111 for no loss at close on an eventful third day with the visitors still trailing by 219 runs.
With two full days left in the match, India still hold the advantage of going 1-0 up in the four-match series. England will have to bat out of their skin to save the game on a Sardar Patel track that appears to be getting slower.
The visitors showed better application in the second innings, after India, who scored a massive 521 for eight declared, asked them to follow-on.
Left-arm spinner Ojha claimed his career's fourth five-wicket haul with figures of five for 45 in 22.2 overs in his 17th Test while Ashwin grabbed three for 80 in 27 overs.
Starting the second innings after an early tea, Cook and debutant Compton, who was out for nine in the first innings, put on an unbeaten century stand to give England a fine start in their quest for avoiding an innings defeat.
Neither Ojha, nor his off-spin partner Ashwin, could pose as many problems to the English openers in the second essay as they did in the first.
The spinners, especially Ashwin, also bowled a lot flatter and did not stick to a consistent line of attack on a wicket that became more and more placid as the game progressed.