Two goals from Mark Stallard and one each from Jamie Tolley and Sagi Burton gave the home side the win that lifted them to within three points of a play-off spot.
And although Darren Caskey briefly reduced the arrears shortly after the break, there was no denying Shrewsbury their first ever league win over Diamonds.
With two wins and a highly-creditable draw at third-placed Grimsby from their last three games, Shrewsbury went into this vital encounter in confident mood.
And their new found belief wasn't misplaced as Stallard made the breakthrough after just seven minutes, netting with a close-range angled drive when the Rushden defence failed to clear their lines.
With just two draws and six defeats from their previous eight meetings with Diamonds, Shrewsbury were keen the break the sequence which became even more likely when midfielder Tolley side-stepped two defenders and fired home from 20 yards on 36 minutes.
At this stage it appeared second bottom Rushden would be swept aside with ease, but Barry Hunter's men began the second half in determined fashion and cut the lead with Caskey's smart free-kick two minutes after the restart.
But any hopes of securing a much-needed point all but disappeared in the 55th minute when Stallard pounced on more poor defending to easily net his sixth of the campaign.
The issue was put beyond all doubt nine minutes from time when Burton crashed home a header from Tolley's corner.