Vijay, 30, scored his fourth test century and first outside India with an assured display as wickets fell around him, hitting 20 fours and one six off 294 balls.
The opener was given sporadic support from his team mates who struggled to establish themselves at the crease, before he was joined by captain Mahendra Singh Dhoni (50 not out) after tea, the pair putting on an unbeaten 81 for the fifth wicket.
England struggled with the slow pitch in Nottingham but took wickets at the beginning of each session to ensure they kept India within touching distance in good batting conditions at the start of the five-test series.
"I've worked a lot with videos of James Anderson," Vijay told Sky Sports. "The first 15 minutes are the toughest thing as an opener. I wanted to play straight and late. It's a good batting wicket. After lunch, there was a period when it was doing a bit, so that was a good experience for me."
On a flat morning England's pace attack struggled to impose themselves, with Anderson taking the solitary wicket of Dhawan (12) before lunch when an outside edge was well-taken by wicketkeeper Matt Prior.
The hosts, looking for their first win in nine tests and the first of coach Peter Moore's second spell in charge, were a different side after lunch and took two wickets for one run in the first three overs. Anderson removed the impressive Pujara (38), who had shared a second-wicket stand of 73 with Vijay, when Ian Bell took a brilliant one-handed diving catch at silly mid-on. Stuart Broad then had Kohli (1), widely considered India's biggest threat with the bat, caught at second slip by Bell to reduce India to 107 for three. India rallied with a fourth wicket stand of 71 before seam bowler Liam Plunkett took the wicket of Rahane, who had looked comfortable working his way to 32.
England's under-pressure captain Alastair Cook, having overseen a 1-0 series loss to Sri Lanka last month and an embarrassing 5-0 Ashes defeat in Australia earlier in the year, caught Rahane when he mistimed a pull shot.
Dhoni ensured there was no further damage however, playing some extravagant shots to reach 50 off 64 balls to help lay a solid platform for his side.
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