Batting first, Prakash Jayaramaiah made useful 42 while vice-captain Ajay Kumar Reddy contributed 25, helping India to post a competitive total.
For Pakistan, Mohammed Jameel scored a quickfire 47, Ali Murthaza struck 38 while Mohammed Akram helped himself to 32 runs.
Having won eight matches on the trot in the group stage, Pakistan could not maintain the winning streak when it mattered most.
India had only lost to Pakistan in the group stage and thrashed Sri Lanka in the semi-final.
Pakistan had spanked England by nine wickets in the semi-finals.
The victory is India's first in a World Cup final after they lost to Pakistan in 2006.