After restricting India for 316, England raced to 216/1 at stumps only 100 runs behind the hosts. Cook (136 not out) and Jonathan Trott (21 not out) were at the crease.
Cook continued his dominance over the Indian bowlers and posted his third century of the series and partnered a stoutly defending Nick Compton (57) to take England in a resounding position.
Cook's magical innings saw him reaching several batting milestones. On 88, the 27-year-old southpaw became the youngest ever batsman to reach 7,000 Test runs. The previous record was held by Sachin Tendulkar who reached the milestone at 28.
He swept offie Ravichandran Ashwin for three in the 52nd over to reach the magical three-figure mark and in the process surpassed England greats Wally Hammond, Geoffrey Boycott and Colin Cowdry to become the first England batsman to score 23 test centuries.
India's only success came in the 53rd over when trying to sweep Prgayan Ojha, Compton, who scored his maiden test fifty, was adjudged leg before. There was also some excitement after umpire Rod Tucker initially shook his head in the negative before raising his finger. Cook and Compton stitched together a first wicket partnership of 165 in 53 overs.
Trott then joined Cook in the middle and the duo took England past 200.
Indian captain Mahendra Singh Dhoni kept juggling his bowlers but the English batsmen defended firmly and punished the loose balls. All the Indian bowlers including Ojha looked mediocre and failed to trouble or contain the visitors.
English pace spearhead James Anderson in the first innings consistently posed problems for the Indian batsmen with his reverse swing but the home team's fast bowlers Zaheer Khan and Ishant Sharma failed to impress.
In what seems to be a rerun of the Mumbai test where India were handed a humiliating defeat, England, who began their innings cautiously, gradually consolidated their position grinding runs as the host bowlers looked nowhere near threatening.
With the pitch playing true, the Indian attack struggled to make inroads. The only chance that came India's way was in the 20th over but Cheteswar Pujara at first slip could not hold on to the ball edged by Cook off Khan.
Cook, who has so far amassed over 400 runs in the series, was then at 17 with the England score being just 27.
While the rest of the bowlers failed to put any impression, Dhoni held back Ojha, by far the best Indian bowler in the series, till the 26th over.
Ojha has taken 14 wickets in the last two tests of the series.
Cook and Compton attacked the Indian spinners, with both hitting a six each, not allowing them to settle down. The duo brought England's 100 in the 36th over with Cook scoring the lion's share.
Earlier, Indian skipper Dhoni hit his 27th Test fifty as the hosts were bowled out for 316 runs before lunch.
India resumed at the overnight score of 273/7, but England bowlers took the three remaining wickets in quick time to hold back the hosts from getting to a sizeable total.
Steven Finn dismissed Dhoni at 52 to end the Indian innings, 62 minutes into the morning session. The skipper batted well with the tail to continue his good run at the hallowed stadium where he has scored two of his Test centuries.
With wickets falling at the other end, Dhoni upped the ante and hit consecutive sixes off Panesar and in the process brought the team's 300.
Panesar, the first Sikh to play for England, had devastated India in the previous Test in Mumbai, and continued to do the good work in the morning, sending back Zaheer (6) and Ishant Sharma (0) in successive overs.
Panesar (4/90) emerged as the most successful bowler while Anderson returned with figures of 3/89, including the wicket of Tendulkar.