Otago got their chase off to a rollicking start as openers Brad Wilson and Michael Rippon cruised to a 63-run partnership.
Rippon was the aggressor of the pair but lifted a flick of the pads to the waiting hands of Daniel Flynn, ending his innings on 43.
Off-spinner Walker (2 for 97) looked the most likely of the Northern Districts attack, while James Baker (1 for 69) accounted for Michael Bracewell for just two.
Walker then forced an edge from Derek de Boorder (3), which Daryl Mitchell took on the second attempt. With Otago at 94 for 3, the match was delicately poised.
However, Kitchen arrived at the crease to pair with former Kaipara Flats and Northland batsman Wilson and the pair went about counter-attacking the Northern Districts attack.
The pair eased their partnership past 50 and were looking good for twin centuries before a direct hit from Tim Seifert removed Wilson for 74.
Kitchen carried on and never looked flustered, calmly leading his side home.
He smashed 10 boundaries and three sixes as he paced himself to first-class century number eight.
Sean Eathorne played a nice cameo of 28, before Kitchen saw Otago to victory with 10 overs left in the day.
The result lifts Otago off the foot of the ladder, while Northern Districts will keep top spot if neither Canterbury or Wellington can force an outright win.
*To see photos, turn to A35