Northants rocketed through the morning session, scoring 160 runs in just 29 overs, before Adam Rossington (78) fell after lunch.
Olly Stone (60) registered his highest first-class score as his record 10th-wicket stand with Monty Panesar pushed Northants to 498.
Panesar dismissed Tom Latham (24) but Kent closed on 88-1, trailing by 14.
The bat continued to dominate as Northamptonshire and Kent's bowlers struggled to make an impact.