League Two's top scorer Karl Hawley was in devastating form, scoring twice and setting up two more in the Cumbrians' five-star showing.
But it was strike partner Derek Holmes who started the rout with a simple header after just 42 seconds. Chris Lumsdon's corner found Holmes unmarked six yards out and the strapping Scotsman barely lifted his feet off the ground to give his side the perfect start.
Carlisle dominated with the only surprise being that the margin of victory was not bigger.
Rushden gifted a goal after 33 minutes when Holmes' pass left Hawley clear and he made no mistake from 15 yards.
Hawley then hit a post from close range, but made amends with a great solo strike four minutes after the break. Picking up Danny Livesey's clearance Hawley ran at two defenders, checked back and wrong-footed them both, before firing an unstoppable shot past Dan Crane for his 21st of the season.
Diamonds midfielder Petr Mikolanda almost snatched a goal back but his ten-yard volley was acrobatically saved by Keiren Westwood, who saved again from the resulting corner.
But the home side soon found their scoring touch again with two near identical goals within 60 seconds of each other. Hawley shielded the ball on the edge of the box, allowing sub Simon Hackney to run on to his pass and volley into the top corner from the edge of the box for his first ever league goal.
Rushden surrendered the ball from the kick off and, with Hawley again holding the ball up; Hackney again pounced to make it five with a low shot past the despairing Crane.
Wayne Hatswell headed just over for Rushden late on, but Westwood's goal was never really in danger, as the sides look destined to leave League Two in different directions this summer.