After finding themselves behind to an early goal in two of their last three League Two encounters - all of which they have failed to win - it was Shrewsbury who made the early breakthrough.
And although bottom of the table Luton fought hard, there was only ever one likely outcome, with two late strikes from the home side putting the issue beyond any doubt.
Midfielder Paul Murray opened the scoring on four minutes and despite being kept at bay by Mick Harford's men for the next 70 or so minutes, goals from skipper Ben Davies and then top scorer Grant Holt saw Town to victory with a minimum of fuss.
Starting his first game since August due to injury, Murray wasted no time in announcing his return - and when the Luton defence failed to clear their lines in the fourth minute, he drilled the ball home from the edge of the box, his low shot beating the despairing dive of Hatters keeper Conrad Logan.
There were chances aplenty as Paul Simpson's promotion hopefuls dominated the remainder of the first half - with Holt, Davies and Kevin McIntyre all going close to increasing the lead, with a long-range effort from Paul McVeigh that was tipped over by Shrews' goalkeeper Glyn Garner, all the visitors could muster in reply.
In the second half Shrewsbury continued to press in order to make the game safe, but they were frustrated in their efforts until 14 minutes from time, when Davies crashed home his ninth of the season with an unstoppable angled drive from 12 yards.
Backed throughout by a vociferous following, there was now no way back for Luton and their misery was compounded in the 87th minute.
Holt turned home a Richard Walker cross from close range, his 11th goal of the campaign completing the scoring.