But the England captain, under intense pressure as he seeks a first Test century in 28 innings and his team try to arrest a run of seven defeats in nine matches, fell just short of a century, managing 95 before being caught by his counterpart MS Dhoni from the bowling of Ravindra Jadeja.
Cook might easily have gone cheaply again earlier in the innings after winning the toss on a bright but cloudy morning.
Instead, he survived on 15 when he poked out at a Pankaj Singh delivery from round the wicket and should have become the debutant's maiden Test victim, only for Jadeja to put down a straightforward chance at third slip.
He and Robson were therefore able to share an opening stand of 55, towards a promising 78 for one at lunch.
Cook often appeared tentative, edging the first ball of the match from Bhuvneshwar Kumar short of second slip and also beaten on the outside edge by Mohammed Shami before his scare against first-change Pankaj.
He nonetheless went past Kevin Pietersen into fourth place among England's all-time Test runscorers when he drove Shami past cover for three to go to 22.
Robson was more convincing, with cover-driven fours off Kumar and then Shami, until the latter saw him off with a touch of extra bounce - Jadeja safe this time with the mirror-image chance at third slip.
Cook cracked on, though, and hinted at growing confidence by cutting Kumar authoritatively for his second boundary, at the start of the seamer's second spell, on the way to his highest score in 10 innings since his half-century in the Melbourne Test last Christmas.
He was joined at the crease by Gary Ballance, who, after the captain's dismissal, continued to build on his scratchy innings and did manage a century, scoring 104 not out by the end of play.
On a pitch with pace and carry, England were doubtless a little relieved to discover there would be no threat from Ishant Sharma - the tall seamer who helped to put India 1-0 up at Lord's six days ago but is injured here.
Pankaj therefore got his opportunity, while England made two changes to their pace attack - Chris Woakes and Chris Jordan replacing Liam Plunkett and Ben Stokes.
- Sports & Recreation
- Ravindra Jadeja
- Bhuvneshwar Kumar
- Mohammed Shami