Jones stuck the winner in only the third minute after curling a perfect free-kick into the top left-hand corner from 20 yards after Simon King had been penalised for hand ball.
Gillingham pressed forward in search of an equaliser but never really troubled Town goalkeeper Mark Bunn over the 90 minutes as they fell to a disappointing defeat.
After Jones had struck, the visitors came within inches of doubling their lead on 23 minutes, but Jason Crowe's close-range effort crashed back off the crossbar from Danny Jackman's cross.
The home side finally roused themselves and carved out two decent chances within minutes.
First Mark Bentley headed John Nutter's free-kick just wide, before Adam Miller turned and clipped a half-volley onto Bunn's crossbar.
A minute before the interval a slight hesitation between Bunn and Crowe allowed Delroy Facey to reach Gary Mulligan's flick, but the burly striker could only poke his shot wide.
Gillingham piled forward in the second period but it was the Cobblers who continued to create the better opportunities.
Ryan Gilligan lashed inches wide of the far post on 53 minutes from Dean Bowditch's pass and ten minutes later, Bowditch had the freedom of Gillingham to meet Jones' cross but headed tamely wide.
Gillingham threatened to punish that miss but, despite enjoying plenty of possession, could not break down the resolute Northampton defence.
But with ten minutes remaining, the home side felt they should have been awarded a penalty but referee Andy D'Urso waved away their claims despite Jackman appearing to handle in the area.
Gilligan missed another great chance to kill the game off moments later but lacked composure in front of goal when he needed it most.
But it was not to prove costly as Gillingham were unable to find a way through despite desperate attempts in the closing stages.