Opting to bat first, Northamptonshire lost wickets at regular intervals but comeback man Chris Rodgers, who replaced Sourav Ganguly, struck a 65-ball 59 and then Bilal Shafayat (91) and Ben Phillips (65) steadied the ship.
Both the batsmen played positive cricket and tackled the Surrey spin trio of Kumble, Nayan Doshi and Ian Salisbury with aplomb.
Kumble tasted blood when he induced Usman Afzaal (13) for a drive to catch him off his own bowling.
Lance Klusener (31) was looking well set and dangerous but Kumble removed the southpaw and finally he dropped curtains on Ben Phillips' 102-ball knock of 65, when the batsman holed out to Ian Salisbury.
Kumble's figure in the match read 28-10-83-3, while Salisbury too came up with a three-wicket haul. Nayan, son of Dilip Doshi, claimed two for 42 in his 16 overs.
This was the first time since 1959 that Surrey fielded a three-pronged spin attack.
In another division two match, Zaheer Khan struck three fours in his 10-ball knock of 13 as his side Worcestershire reached 438 for nine against Glamorgan at Colwyn Bay.