The Reds walked away with it to record a first away victory of the season at the fourth attempt, but it was hardly a convincing start.
For the second successive away outing, Wrexham struggled to get going and, just as they did at Altrincham on Monday, fell behind to an early goal.
Salisbury went into the game as leaders after four successive wins and Wrexham, on the back foot, could not come to grips with the home side's blistering start.
As the first half wore on, Wrexham improved and Shaun Whalley equalised two minutes before the break.
But the big improvement on Monday's draw at Altrincham was Wrexham's response after the interval.
Wrexham took the game to their hosts and were in control for the whole of the second half.
There was no let up from Wrexham who attacked with purpose and they were rewarded with three more goals as Salisbury not surprisingly began to tire.Jefferson Louis took his tally to the season to five with a double, with his first taking a wicked deflection, and Whalley got his second.
It has been rare over the last two years of struggle to see Wrexham recover from going a goal behind and to run out winners. Very rare.
The 4-1 margin means that Wrexham, up to fifth in the table, boast the best goal difference in the Blue Square Premier.
Wrexham are the second highest scorers - only Burton Albion, tomorrow's visitors to The Racecourse and 5-2 winners over Lewes at the weekend, have more - and the Reds have also conceded the least amount of goals along with Salisbury and Kettering.
If Wrexham continue to keep performing like this at both ends of the pitch, and on their travels as well as The Racecourse where they boast a 100 per cent record, there is no reason why the Reds can't challenge for promotion.
Little made three changes to the side that drew at Altrincham in the previous outing.
Kyle Critchell was ruled out with an ankle ligament injury sustained in training on Thursday, while Levi Mackin and Sam Aiston were relegated to the substitutes bench.
That meant a new look Reds' midfield with Wes Baynes lining up on the right,and Nat Brown, having been ruled him out for three matches with a groin strain, switching to the centre of midfield after starting the campaign in defence.
And Simon Brown was recalled to the side in an attacking role - his preferred position despite previously featuring on both wings - meaning Shaun Whalley switched to the left of midfield.
Nat Brown shot well wide of the target in the opening exchanges, but he had clearly not fully recovered from injury and was forced off after eight minutes.
But substitute Mackin's first involvement in the game just two minutes laterled to Salisbury's opening goal after he brought down Matthew Tubbs on the edge of the area.
Striker Andrew Sandell struck the free-kick which took a wicked deflection off Baynes and beat keeper Gavin Ward, who had already dived the other direction.
Salisbury were on top and making all the running, with Sandell and Tubbs both firing into the sidenetting.
Wrexham were struggling to make an impact in the final third, summed up byLouis mis-cueing after being put through by Simon Brown when he should have done better.
Whalley put Simon Brown through on goal after 27 minutes and his low drive beat keeper James Bittner but was turned behind by Timothy Bond despite heading wide.
And from the resulting corner, Steve Evans saw his close range effort blocked for another corner by Bittner.
However, there was no sign of Salisbury easing up and Tubbs brought an excellent save out of Ward after meeting Sandell's knock down.
There was an improvement from Wrexham as the half wore on and Simon Brown sent Baynes through on goal but he was denied by Bittner.
And Wrexham were back on level terms two minutes before the break.
Carl Tremarco's quickly taken throw in was seized upon by Whalley who was given plenty of space and allowed to run in at goal, and his curling drive from outside the area sailed past Bittner.
Determined to push on after the equaliser, Wrexham were quick out of the blocks at the start of the second half and Louis was able to take a cross down before smashing narrowly wide of the mark.
And the Reds took a 2-1 lead on 54 minutes. Simon Spender crossed from right and although Louis's header was missing the target, the ball deflected off Darrell Clarke and found the bottom corner.
Salisbury assistant manager Barry Blankley was immediately sent to the stands by referee John Farries for comments made.
There was a renewed confidence about Wrexham who had completely dominated since the break.
And Wrexham went 3-1 ahead in the 76th minute. Spender's long clearance fell for Louis on the halfway line, and the big striker shrugged off home captain Aaron Cook on route to goal before slotting past Bittner.
That was not the end of the scoring as Wrexham made it 4-1 in the first minute of injury time.
Whalley was allowed to run at goal and his 20 yard shot took a kind deflection off Matt Robinson and looped over Bittner.
That sealed victory and a welcome away day win for the Reds.
Ask Brian
If you have a question for Brian Little email it to digitalnews@nwn.co.uk and we'll ask as many as we can during our next video interview with the Reds boss this Thursday.
The full article contains 960 words and appears in n/a newspaper.