The tourists won the first match of the currrent series by an innings and 52 runs as Pakistan, following on 268 runs behind, were dismissed for 216 in their second knock in the second over on the fifth and final day on Thursday.
In previous tours of Pakistan between 1954 and 1989, India had lost five Tests and drew the remaining 15 in what is regarded as the ultimate rivaly in world cricket.
Pakistan added nine runs to their overnight score of 207 for nine when Yousuf Youhana (112) was caught at mid-wicket by stand-in captain Rahul Dravid off left-arm seamer Irfan Pathan.
India, who rode on Virender Sehwag's 309 and an unbeaten 194 from Sachin Tendulkar to hit 675 for five declared, bowled out Pakistan twice on a barren wicket slammed by critics as being heavily tilted in favour of batsmen.
India went into the match without regular captain Sourav Ganguly and two top bowlers Ashish Nehra and Harbhajan Singh who were all injured.
Then left-arm seamer Zaheer Khan suffered a hamstring injury on the fourth day and was unable to bowl in the second innings.
Zaheer, like Ganguly, has been ruled out of the second Test starting at Lahore's Gaddafi stadium on Monday.
The third and final Test will be played at Rawalpindi from April 13.
The depleted Indian attack was carried bravely by seasoned leg-spinner Anil Kumble and rookie seamer Pathan, playing only his third Test.
Kumble, who once took all 10 Pakistani wickets in a Test match in New Delhi in 1999, returned to haunt the arch-rivals with 6-72 in the second innings which lifted his career tally to 390 from 82 matches.
Pathan, 19, followed a career-best 4-100 in the first innings with 2-26 in the second.
"It is fantastic to lead such a gallant side," said Dravid.
"It was a great team effort. Sehwag and Sachin were outstanding with the bat as we know them to be.Our bowling attack is young and inexperienced but they showed great heart and a will to fight on a wicket that was not easy to bowl on. Kumble was simply magnificent.We will celebrate as we should after such a great win, but our feet are on the ground. We know Pakistan will come back hard in the remaining two Tests, but we will be ready for that."
Pakistan captain Inzamam-ul-Haq said India played the better cricket and deserved to win, but stressed his team was not disheartened by the loss.
"A good session at Lahore will help us to bounce back in the series. We have done it in the past and I am confident we will do it again," he said.
It was India's second innings victory over Pakistan, following the innings and 70-run win in the inaugural Test between the two countries in New Delhi way back in 1952.
In the ongoing tour, India won the preceding One-day series 3-2.