Brook, fresh from scoring an unbeaten 91 in the Roses T20 game last weekend, scored 113 to help set the hosts a challenging 206 to win on a turning surface.
Northants' reply got off to the worst possible start as Yorkshire captain Steven Patterson claimed two early wickets either side of lunch to spark a collapse with four wickets falling for just 11 runs.
Spinner Dom Bess also picked up two victims to extend his match haul to nine and further underline his case for an England recall.
Tom Taylor provided the home fans with some late entertainment with some big hitting, but when he fell for 40, only Luke Procter and Simon Kerrigan provided any resistance as the hosts finished 152 all out.
The win sees Yorkshire further cement their grip near the top of group three of the LV= County Championship, and ends Northants' chances of claiming a top two finish in the LV= Insurance County Championship.
Brook was in imperious form in the morning against some tight bowling from Kerrigan and Ben Sanderson who made an early breakthrough when he enticed an edge from Jordan Thompson.
Patterson showed some resistance, but could only fend a short-pitched delivery from Sanderson to Emilio Gay at short leg who took a brilliant diving catch to leave Yorkshire on 189 for eight.
Brook who reached his century from 168 deliveries, went on the offensive as wickets fell at the other end, swatting Kerrigan straight back down the ground for his eleventh boundary before falling next ball to give the spinner his fifteenth five-wicket haul as Yorkshire finished on 217.
Northants were soon in disarray as they lost three wickets for just two runs either side of lunch.
Stand-in captain Ricardo Vasconcelos fell lbw playing forward to Patterson just before the interval.
Then in the second over after lunch Charlie Thurston picked out short leg to give Patterson his second wicket. Next over, Gay drilled Bess straight to short cover to leave the County in dire straits at 19 for three.
Bess got the ball to turn across Rob Keogh and take the edge through to short-leg, then Adam Lyth held onto a sharp, low catch at slip offered by Saif Zaib to leave Northants five wickets down with just 43 on the board.
Taylor decided to counterattack, striking eight boundaries and drilling the seamers firmly back down the ground, sweeping Bess and scooping Ben Coad back over the keeper’s head.
But when he was trapped lbw by Coad, Northants were 87 for six, still 108 adrift. Procter and Kerrigan raised home hopes with a stand of 49 but ultimately finished short.