Aldershot moved 17 points clear at the top of the table and are now on the brink of returning to the Football League after a comfortable victory.
Anthony Straker set Rob Elvins up to slot home the opener from close range.
Ben Harding was denied a second by a fine save from Salisbury keeper Ryan Clarke before Liam Feeney's close-range effort brought the visitors level.
But the Shots restored their advantage when substitute Daniel Hylton headed home from close range.
Aldershot: Bull, Gier (Hylton 70), Day, Charles, Straker, Soares, Chalmers (Donnelly 66), Harding, Hudson, John Grant (Newman 78), Elvins.Subs Not Used: Mendes, Jaimez-Ruiz.
Goals: Elvins 3, Hylton 82.
Salisbury: Ryan Clarke, Robinson, Cook, Bond, Bartlett, Turk, Sinclair, Feeney, Darrell Clarke, Sandell (Barnes 39), Tubbs.Subs Not Used: Fowler, Brown, Bass, Bittner.
Booked: Tubbs, Darrell Clarke, Cook, Barnes.
Goals: Feeney 61.
Att: 3,388
Ref: M Bull (Essex).
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