John Dempster's goal was enough to defeat York and give new Kettering manager Marcus Law his second victory in two games.
Dempster scored with a powerful header from Jean-Paul Marna's pin-point cross early in the second half.
Kettering had further chances but Paul Furlong shot over from inside the area and Marna fired wide from 20 yards out.
York substitute David Dowson volleyed over with the hosts' best opportunity as they failed to grab an equaliser.
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York:
Ingham, Parslow, McGurk, Young, Meredith, Till, Barrett (Smith 67), Lawless, Fyfield, Constantine (Dowson 62), Beesley (Gash 62). Subs Not Used: Knight, Courtney.
Booked: McGurk.
Kettering:
Jack, Noubissie, Graham, Dempster, Taylor, Dance, Boucaud, Solkhon, Makofo (Kelly 90), Furlong (McKoy 76), Marna. Subs Not Used: Cooper, Westwood, Roper.
Booked: Dempster, Dance.
Goals: Dempster 51.
Attendance: 1,978
Referee: D Mohareb (Cheshire).
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