The 30-year-old Vijay (122 not out) notched up his his fourth Test century and batted right through the day to steer the visitors to a comfortable position after being reduced to 107 for three just at at the start of the second session at Trent Bridge.
Captain Mahendra Singh Dhoni (50 not out off 64 balls) was giving Vijay company at close on an absorbing opening day's play.
Vijay decorated his 294-ball stay at the crease with 20 boundaries and one six, while Dhoni struck five fours en route to his half-century knock.
Live Commentary India vs England Trent Bridge Test:
The duo shared unbeaten 81 runs for the fifth wicket, digging India out of trouble after some fine rearguard fourth-wicket partnership of 71 runs between Vijay and Ajinkya Rahane (32 runs off 81 balls, 4 fours) in the post-lunch session.
But India witnessed a scare just after lunch as they lost Cheteshwar Pujara (38 off 69, 7 fours) and Virat Kohli (1) in quick succession to reel at 107 for three at one stage.
James Anderson (2/70), Stuart Broad (1/26) and Liam Plunkett (1/56) were the only wicket-takers for England.
In the post-tea session, Vijay resumed his innings at 92 in the company of Rahane. But the latter didn't last long, getting out in a freak manner soon after the break, bottom-edging a short delivery from Liam Plunkett to captain Alastair Cook at silly point.
The dismissal brought an end to their 71-run fourth-wicket stand that lasted 27.1 overs and saved India the blushes.
The England attack then tried putting pressure on Vijay as he neared his hundred but were unsuccessful as he maintained his composure.
But his single to get to the three-figure mark was anything but calm as a frantic nudge to square-leg put Dhoni in danger, though the India skipper survived.
Vijay registered his fourth Test century off 214 balls, with the help of 18 fours, in the 68th over. It was his first Test hundred outside India and the first against an opposition other than Australia. It was also the 100th Test hundred scored at Trent Bridge.
Dhoni, on the other end, played some attacking cricket and hit lusty boundaries by using his powerful bottom-hand.
He brought up his 30th Test fifty in the final over of the day.
As in the first two sessions, once Anderson and Broad went off the attack, the other bowlers Ben Stokes (0/47), Moeen Ali (0/50) and Joe Root (0/6) failed to make any impression.
India's 200-run mark came up in the 70th over of the day. Vijay and Dhoni batted sensible to get to their 50-run partnership in the 77th over of the innings.
Earlier starting the post-lunch session at 106 for one in 30 overs) with Vijay (55 batting) and Pujara at the crease, India lost two wickets quickly as to slump to 107 for three from 106 for one as Anderson and Broad found some reverse swing.
Pujara was the first to go, in the second over after lunch, as the delivery from Anderson jagged in and took off with Ian Bell at silly mid-on completing a stunning one-handed catch diving to his right. India's number three batsman departed without adding to his tally.
Vijay and Pujara had put on 73 runs for the second wicket in the morning session as the English bowlers found the going tough on a placid wicket.
It became a massive double blow when Kohli was out in the very next over. Broad got Kohli with one that left him minutely and took the bat's edge falling straight to Bell at second slip. Suddenly India were tottering at 107 for three and with just six batsmen playing and things didn't really look cosy.
Then walked in Rahane who had to spend some tense moments at the crease. At the other end Vijay stayed put as the two batsmen played out this tough period. As a result the scoring rate suffered with only 18 runs coming from 14 overs bowled in the first hour after lunch.
But it didn't matter much as the fall of wickets was controlled and with the strike-bowlers going off, the pair brought up their 50-run partnership in the 54th over of the innings.
In the morning session, India won the toss and elected to bat first. Vijay opened the innings with Shikhar Dhawan (12 runs off 24 balls) as they looked to make full use of the handsome batting conditions. It was a change in roles for the two batsmen, as Vijay was the one off to a flier with a flurry of boundaries while Dhawan played carefully and looked to make a solid start.
Dhawan was out caught driving to Anderson who went round-the-wicket and changed the angle, with keeper Matt Prior completing a brilliant catch. It was the 50th Test wicket for the bowler at Trent Bridge, outlining his super record at this ground even though he struggled on the day.
After that there was no respite for the English attack as Vijay was joined in by Pujara at the crease, and the two played solid and watchful cricket. The runs started flowing as the field began to spread. The 50-run mark came up for India in the 13th over just before one hours play was completed.
Vijay then brought up his fifth Test fifty, off 68 balls with 11 fours, in the 24th over and two overs later, the 100-run mark came up for India.
Earlier, India handed a Test debut to all-rounder Stuart Binny, choosing to play five bowlers, and dropping Rohit Sharma to make way for him. The Karnataka player follows in his father former cricketer and also current selector Roger Binnys footsteps and the duo became the tenth father-son pair to represent the country in Tests. England too made one change to their eleven from the loss to Sri Lanka at
Headingley, bringing in fit-again all-rounder Ben Stokes in place of Chris Jordan.