The Cobblers effectively sealed their victory by half time with Martin Smith's 10th goal of the season and a first for the club by skipper Ashley Westwood seven minutes before the break.
The home side went badly off the boil after half time and allowed a moderate Shrewsbury side half a chance of clawing their way back into the contest.
The closest the visitors came was in the 63rd minute when a venomous Neil Ashton volley was blocked on the line by Scott McGleish.
Shrewsbury's disappointing Easter - they were held by Cambridge on Friday - was made worse in the closing minute when Stuart Whitehead was shown the red card by referee Paul Armstrong for hauling back substitute Lee Barnard after being booked in the first half for a foul on Fred Murray.
Northampton took the lead in the 16th minute when a cross by Sam Togwell, who was making his home debut after signing on a month's loan from Crystal Palace, caused chaos in the visitor's defence.
The ball eventually fell to Smith who poked in a left-foot shot from 12 yards to continue his scoring flurry which has been all the more remarkable as his first didn't come until late October.
Shrewsbury almost equalised when Ashton's corner was met by the head of Darren Tinson but Murray cleared off the line.
Jake Sedgemore curled a free-kick on to the roof of the net but the home side gave themselves a cushion when Westwood had the simple task of running in a Smith corner from close range.
Not only was it the first time Northampton have scored from a corner this season it was also their first goal contributed by a defender.