Town took the lead in the 10th minute with Paul Harsley's 30 yard free kick, which was heavily deflected past Paul Bastock. It was no more than the Cobblers midfielder deserved following some stunning performances this season.
Minutes later Jamie Forrester chipped a 25 yard effort just over the crossbar as Town began to take control and Derek Asamoah drilled a low shot wide from just outside the penalty area.
Marco Gabbiadini scored his 10th goal of the season on 35 minutes, powering home a Chris Carruthers cross from close range.
The visitors came into the game in the second half and were rewarded with a penalty in the 56th minute, Richard Hope clumisly tripped Lee Thompson and ex-Cobbler loanee Tony Battersby only just beat Lee Harper.
With Boston's tails up, Town defended well and restored their two goal advantage on 68 minutes. Gabbiadini made another at the Pilgrims defence, the ball broke to Derek Asamoah who cooly finished past Bastock.
With 8 minutes left on the clock, Alex Higgins headed home to give the visitors hope, but the Cobblers held on to go through.
As the players left the field, Ray Warburton recived a massive ovation from Cobblers fans, it was an emotional return for the former Cobbler. The only downside of the day for the Cobblers is the news that Paul Rickers has broken his left leg following a crunching challange in the first half.
NTFConline Man of the Match
Marco Gabbiadini - another classy perfrmance and another goal.
Ref Watch
Steve Baines wasn't Town's favourite when he refereed the Wigan league cup tie. Today he was much better but failed to let the game flow by ignoring advantages and pulling play back. The Boston fans, who were load throughout the game, felt hard done by Baines, but appeared harsh on him.