At draw of stumps, Goa in their second innings were 11 for no loss with Sagun Kamat and Rohan Balekar unbeaten on 4 and 7 respectively.
Resuming at their overnight score of 134 for one, Assam came close to overhaul Goa's first inning total of 381 but some brilliant bowling by Jakati and two run-outs saw them all out for 366 as the match is heading for a draw with only one day remaining.
Jakati first got the break through when he had A S Sinha leg before for 39.
S A Roy who battled resolutely and shared second wicket partnership of 95 with Sinha looked set to score a century but was caught by Ravikant Shukla off Rahul Asnodkar for 87.
Dhiraj Jadhav took the fight to the rival camp but two run-outs spoiled Assam's chances of taking the lead as wickets fell at regular interval.
Jadhav was out for 52 caught by Bisla off Gawas.
Jakati then dismissed A N Ahmed (18) and A Konwar (0) to end Assam hopes of going into the knock out stage.
While Jakati claimed four wickets, M G Gawas took two and R D Asnodkar claimed one wicket.