Goals from Michael Hughes and Jobi McAnuff, followed by two second-half penalties from Andy Johnson and Dougie Freedman, ensured the Eagles secured their fifth consecutive win.
A lively match ensured good cup tie entertainment for the crowd of 10,000 who braved the damp cold south-east London weather.
Hughes gave the Eagles a great start after Northampton needlessly conceded a free-kick just outside the box. Skipper Hughes drove low through the wall and wide of Lee Harper's outstretched arm and into the corner of the net.
Within eight minutes the Cobblers were back in it after a strong run from Andy Kirk led to Josh Low gathering his pass and then coolly slotting past Gabor Kiraly to level the scores.
Urged on by their 3,000 fans Ian Taylor then volleyed wide from 12 yards out with Kiraly rooted on his line. But Palace restored their lead nine minutes before the break.
Hughes' quickly taken free-kick from halfway dropped perfectly to Wayne Andrews wide on the right touchline. The Palace winger past his defender and then travelled along the by-line before crossing beyond the far post for McAnuff to fire home from an acute angle.
The second half began with Kirk heading over the bar but within seven minutes of the half the Eagles put the tie beyond the visitors' reach.
McAnuff made a good run down the left and found Freedman just outside the box. Freedman in turn slipped a pass to Johnson who was brought down by keeper Harper. Johnson, who missed a rare penalty on Monday, this time made no mistake placing his penalty low into the bottom left-hand corner.
Palace took their foot off the pedal and Northampton took advantage by enjoying a good spell of possession.
The Eagles defence remained strong although they were fortunate on a couple of occasions with goalmouth scrambles.
Low and Scott McGleish also had useful chances before Northampton conceded a second penalty two minutes from time after Jason Crowe was harshly adjudged to have handled Tommy Black's byline cross.
With Johnson off, it was Freedman's turn to take the spot-kick and he fired his shot into the top right corner giving Harper no chance.