A 73rd-minute goal from Charles Ademeno denied promotion-chasing Wrexham three points at the Racecourse.
Ryan Flynn gave the home side the lead after just six minutes following delightful build-up play down the right from Marc Williams and Jonathan Brown.
Flynn slotted home from six yards, but in a Salisbury rally after the break Gavin Ward parried a deep Matthew Tubbs cross, and Ademeno headed in easily.
To compound Wrexham's woes Williams went off with a suspected broken foot.
"He's having an X-ray, hopefully it isn't broken but it doesn't look good," Wrexham manager Dean Saunders told BBC Sport Wales.
"If he's not right I'll have to go and get [a striker], maybe two."
Wrexham manager Dean Saunders: "We started great and scored a good goal, but then we missed too many chances, there were probably 10 chances we should have scored from.
"We conceded a really easy goal, but if you don't finish teams off you give them hope. I'm gutted that we haven't won that game.
"We've gone up a place [in the table] which is good, and now we've got to put it right [away at Crawley Town] on Tuesday."
Wrexham: Ward, Curtis, Westwood, Mike Williams, Williamson, Brown, Fleming, Crofts, Flynn (McCluskey 79), Louis, Marc Williams (Suffo 59). Subs Not Used: Collin, Baynes, Fairhurst.
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