The veteran Indian leg-spinner ran through the Northants' middle order in his 34 overs conceding 100 runs as Surrey won the match by successfully chasing the paltry 65-run target set by the visitors.
Northants had won the toss and opted to bat first in the match and were all out for 347 runs in the first innings in which Kumble managed to take just one wicket.
In reply, Surrey piled up 669 for five declared before Kumble, who was brought in late by skipper Mark Ramprakash, came up with a deadly spell to demolish the Northants second innings.
Resuming their second innings on 165-1 on the final day, Northants were reeling but a 78-run ninth-wicket stand between Matthew Nicholson and David Wigley opened up the possibility of an unlikely draw.
But Kumble put paid to any such hopes as he took the wicket of Wigely to break the partnership leaving Surrey with a target of 65 from 14 overs.
The hosts suffered a couple of blows -- when opener Scott Newman fell to the very first ball of the hosts' second innings -- but managed to romp home with skipper Ramprakash making 30.