Rovers never looked back after the big striker Peter Beadle, awarded a penalty after being pushed in the back in the 30th minute by the Town defender Ian Sampson, beat Andy Woodman from the spot.
The former Southampton player Frankie Bennett headed in a Gary Penrice corner seven minutes later to put Rovers 2-0 up. Then, just a minute after half-time, Barry Hayles dribbled past two defenders in the Northampton box before firing home.
The Northampton striker John Gayle pulled one back for the visitors in the 74th minute, but Ian Atkins' men have a big hill to climb on Wednesday to keep their promotion hopes alive.
In the Third Division play-off semi-final first leg at Scarborough, meanwhile, Torquay United grabbed the upper hand with a 3-1 victory.
The St Vincent international striker Rodney Jack fired the visitors into a 22nd-minute lead, only for Scarborough's Jason Rockett to equalise five minutes before the interval.
However, five minutes after the restart, John Gittens reclaimed the lead for the Devon side and then Andy MacFarlane's 72nd-minute strike assured Torquay of a commanding advantage for Wednesday's second leg.
Greg Heald was Barnet's hero as the Bees beat Colchester 1-0 in the other Third Division semi-final first leg at Underhill.
The opening period had been goalless, but Heald beat the Colchester goalkeeper, Carl Emberson, three minutes after the half-time break to give the Londoners the lead.
Barnet's Sean Devine and Guy Branston, of Colchester, were both sent of for violent conduct eight minutes from time.
West Bromwich Albion's 21-year-old striker Lee Hughes, who scored 14 goals in his first season as a Football League player, has pledged his future to the club into the next millennium by signing a new four-year contract.
Arsenal finished as runners-up in the Women's Premier League after beating Doncaster Belles 1-0 at Highbury yesterday.