Pakistan, following on 268 runs behind, were dismissed for 216 in their second knock in the second over of the fifth and final day to give India a 1-0 lead in the three-match series on Thursday.
The hosts 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 Irfan Pathan.
India, who rode on Virender Sehwag's 309 and Sachin Tendulkar's unbeaten 194 to hit 675 for five declared, bowled out Pakistan twice on a barren wicket slammed by critics as being heavily tilted towards batsmen.
In 20 previous Tests on Pakistan soil since 1954, India had lost five and drawn 15.
It was India's second innings victory over their arch-rivals, following the innings and 70-run win in the inaugural Test between the two countries in New Delhi way back in 1952.
India, now on their first full tour of Pakistan since 1989, had won the preceding One-day series 3-2. The second Test starts at Lahore's Gaddafi stadium on April 5, followed by the third at Rawalpindi from April 13.