The Whites had the majority of the game during the first half but couldn't convert their chances.
In the first minute, former Bristol Rovers winger Andy Sandell found himself clear in front of goal but put a weak header straight at Town keeper Nikki Bull.
Bull then did well to block Wayne Turk in a one-on-one situation.
Against the run of play, however, the Shots went ahead on 12 minutes when slack defending allowed John Grant a close-range chance, which he belted into the roof of the net.
Eight minutes later, Sandell was again guilty of a glaring miss when he put a right-foot effort wide of the target from only six yards out.
Salisbury continued to press forward but went further behind when a loose ball in their penalty area was pounced on by Ben Harding for Aldershot's second. Just before the interval, great movement by Turk saw him get clear before firing a fierce left-foot effort which Bull somehow pushed round the upright.
In the second period, chances were rare for both sides, with Salisbury keeper Ryan Clarke making a great save from Harding on 66 minutes, but, 10 minutes before the end, Grant chipped Clarke for Aldershot's third.
In time added on, Bull pulled off a great stop from Sandell but Salisbury had their noses rubbed in it when Grant got his third from what looked like an offside position.
Source: http://www.westerndailypress.co.uk/