Alastair Cook continued to defy India with a historic century as England's faint hopes of saving the first Test remained marginally intact at the Sardar Patel Stadium.

Cook (138no) became the first batsman to make a hundred in his first three Tests as captain, his previous successes as Andrew Strauss' deputy in Bangladesh two-and-a-half years ago before his permanent appointment for this four-match series.

England had conceded a first-innings deficit of 330 on Saturday, and the mission improbable stayed that way, despite Cook's stoic heroics, as wickets fell at the other end on day four - twice in pairs, first for the addition of only four runs and then none when Umesh Yadav put himself on a hat-trick.

Following on, Cook and Nick Compton reprised their century opening stand on Sunday morning - but by teatime, only the captain remained in a total of 264 for five. England lost only Compton in the first hour, to the relief of Mahendra Singh Dhoni who had just missed a chance to stump the debutant opener.

Compton ate up 128 balls and lasted 45 overs for his 37 runs - a handy contribution in the context of the match - before he toppled over in defence against Zaheer Khan's left-arm inswing, and fell lbw.

Jonathan Trott then appeared to be getting himself in, after his first-innings duck, and could hardly be criticised for edging behind on the forward-defence when Pragyan Ojha turned one sharply from a perfect line and length.

Kevin Pietersen has long disputed he has a weakness to left-arm spin, but fell to that variety for the 25th time in his career when Ojha followed up Saturday's success against him. Pietersen got so far across to sweep that he was bowled round his legs by a delivery that took the off bail.

Ian Bell was under extreme pressure after his first-innings golden duck. But he confidently drove his second ball from the same bowler through extra-cover for four, and soon afterwards Cook completed his 181-ball century in more prosaic fashion with a push for two into the leg-side off Yadav.

Bell went in early afternoon, the first of two lbws in two deliveries for Yadav - thanks to reverse-swing, with a ball almost 80 overs old. Both Bell and then Samit Patel could just have easily survived, each time the ball shaping in towards the outer limit of leg-stump, with a suspicion of inside-edge too on the second occasion.

Cook badly needed, and surely deserved, more lasting support as he closed out a third successive session - and until tea, it came in the doughty shape of Matt Prior in an unbroken stand of 65.