Resuming at the overnight score of 146 for seven, the visitors lost the remaining three wickets while adding just 12 runs to their total.
Burdened by a first innings deficit of 209 runs and following on, Assam folded up for 158 in their second knock.
Punjab had scored 422 all out in their first innings while Assam made 213.
The main architect of Punjab's win was Gagandeep Singh who ended with a match haul of 6/26. Rajesh Sharma 2/42 and Navdeep Singh 2/44 were the other wicket takers.
Overnight batsman A Konwar (12) was the first to go when the board read 156. The other overnight batsman SV Saravanan (69, 4x9, and 6x1) was the next to go while Javed Zamman (0) was the last to return to the pavilion.
Punjab got five points from this win.