Now unbeaten at home since the opening day of the season, goals from Mark Stallard, Neil Sorvel and Neil Ashton secured victory for the home side - although Stallard's sixth minute opener had been cancelled out by an excellent long-range free-kick from Phil Stamp 30 seconds before the break that brought Darlington level at half-time.
The two encounters between the sides last term each brought big home wins and another looked on the cards when Stallard struck in the early stages.
Pouncing on some hesitant defending, he struck a low drive to net his third goal of the campaign, a shot that beat Darlington keeper Bertrand Bossu for pace at his near post.
Stallard then missed an easier chance to double Shrewsbury's advantage in the 14th minute, heading over from close range after strike partner Colin McMenamin had crossed dangerously into the box.
Six minutes before half-time referee Bob Desmond pulled up with an injury and was replaced in the middle by senior linesman and former Premiership official Paul Danson - and following his award of a free-kick as the interval loomed, Darlington were back on level terms, when Stamp's swinging right-foot curler flew into the top corner of the Shrews goal.
But the home side were only pegged back for five minutes as Sorvel's deflected shot enabled Shrewsbury to regain the lead on 50 minutes.
Darlington knew their luck was right out when Ashton put the outcome beyond doubt in the 68th minute, his drive from the edge of the area also taking a deflection to beat Bossu.
With ten minutes remaining Dave Hodgson's men almost pulled one back, but a strong run followed by a low shot from Simon Johnson, brought a fine diving save from Shrews' teenage goalkeeper Joe Hart.