The home side, now undefeated since Boxing Day, during which time they have only played two home games, struck twice in the first half through Derek Asamoah and Leo Fortune-West to ultimately secure victory.
But this was a hard-working performance throughout from the home side, who continue to close in on a League Two play-off place, while at the same time putting a dent in the hopes of Notts County, whom the Gay Meadow side now trail by just two points, but with four matches in hand.
On a treacherous, heavily sanded pitch, Shrewsbury were generally in control of a sometimes untidy, stop-start encounter that saw referee Trevor Kettle produce the yellow card no fewer than nine times.
With their first genuine attack in the ninth minute, Shrewsbury found the back of the net, but on his full home debut, the much-travelled Fortune-West saw his close range effort ruled out for offside.
Six minutes later as the home side continued to threaten, Asamoah saw his goal bound effort cleared off the line after Notts County goalkeeper Kevin Pilkington flapped at a cross under pressure from Fortune-West. But there would be no such reprieve for Pilkington in the 32nd minute as Shrewsbury finally broke the deadlock.
When Fortune-West headed on a long clearance, Pilkington appeared to have the ball in his grasp, but right on the edge of the area lost possession and from 18 yards and a narrow angle, Asamoah put his side ahead with a cheeky chip.
Worse was to follow for the experienced County 'keeper as, right on the stroke of half-time, he juggled and then let slip a cross from Marc Tierney that Fortune-West could not fail to nudge home from inside the six yard box.
After the break Notts County had a greater share of possession and often forced Shrewsbury onto the back foot. However, when they found a way through the home defence, the Magpies encountered Chris Mackenzie in good form, with the Shrews' keeper pulling off one fine stop in particular to thwart a glancing header from Lawrie Dudfield.
At the opposite end Asamoah was denied by a diving save from Pilkington, as Shrewsbury ran out deserving and comfortable winners.