It was the same story for the Reds, as we conceded another two goals and failed to find the net ourselves.
In the opening stages it was Wrexham taking the game to their hosts and the Blues were on the back foot. After just four minutes their keeper was forced to punch the ball off Bishop's head at the near post.
Great play by Joe Clarke saw him retrieve the ball then beat his man, before setting up Robbie Evans for a 25-yard shot that was saved by James Belshaw.
An early hamstring injury to Joe Anyinsah saw the winger subbed after just 15 minutes, with Adrian Cieslewicz sent into action.
Immediately the young Pole produced a teasing cross that was met by Kevin Thornton, but the midfielder headed wide with Brett Ormerod probably better placed a few paces behind him.
The Reds produced a good spell of pressure on 25 minutes, all started with Ciss’ run on the right wing that fed Evans in the Nuneaton box. He went down, optimistically appealing for a penalty.
The Welshmen kept the pressure up with five Wrexham players involved and it all ended with Evans curling in a great effort from 25 yards that had Belshaw diving full length, but the ball was just off target.
Joslain Mayebi’s first real action came on 28 minutes, when a high ball carried to the back post where Daniel Sleath stabbed it goalwards but the Cameroonian used his legs to block that effort.
A high boot by Brown caught Ashton as they jumped, it was a simple free kick but the home striker reacted to such an extent that a number of players from both sides got involved in a stand off.
Back in the action an Ashton's back header ran out for a corner. As the cross came in, Nuneaton skipper Gareth Dean managed to get the better of Clowes at the back post but put his effort was placed into the side netting.
In time added on, another break by Nuneaton saw Moult chase a long ball on the left wing. As Mayebi raced from his line he forced the striker into a lob that struck an upright, with Ashton then colliding with the same post as he covered back on the line.
The game became a great deal more open as the second half got underway with Adam Walker twice seeing shots fly outside of Mayebi’s left hand post, while at the other end a lovely one-touch passing move from Wrexham ended with Cieslewicz firing high from 25-yards.
On the hour, Bishop got on a high ball to head out to Thornton, the midfielder firing back across the box, but it was a step ahead of Ormerod in front of a gaping goal.
Clowes was then called on to make a great saving tackle on Moult, denying the striker a run at goal when he looked favourite to breakaway on the left.
Having survived a long run by Armson, the ball broke upfield for Ciss to run onto and shoot from distance, but the effort carried over the home crossbar.
With 20 minutes remaining Ashton had to stretch his frame and put the ball out for a corner. The flag kick went deep and Cowan’s resulting header sailed over the visitors’ crossbar.
Shortly afterwards, Thornton set off a 70 yard run following a Nuneaton free kick and he was unlucky to see his shot scrape the far post.
On 74 minutes, the deadlock was broken, when Andrew Brown was left unmarked at the back post to fire home after Sleath had found him with a cross from the left.
Nuneaton pushed forward from the restart and it took a brilliant save by Mayebi to deny Brown's header that looked goal bound all the way.
A change for the Reds came with boss Andy Morrell being introduced for Thornton.
Nuneaton looked dangerous again on 84 minutes, as Moult cut in from the left and fired across the face of the Wrexham goal, forcing Mayebi to tip the ball away for a corner.
Another quick home attack saw Sleath cut the ball back for Moult, but his shot drifted just wide when well placed.
As we came to the end of 90 minutes, a Johnny Hunt corner was flicked on by Ashton, but it came back off the crossbar. The ball dropped back into play but in the follow up it was finally scrambled clear.
Two minutes into added time, as Wrexham pushed men up for a leveller, they were caught on the break and Walker had the space to set up Moult for a second.
Nuneaton might not be the most fashionable name to be at the top end of the table, but they have now lost only three times in 22 games since early February, and while it was more positive display Andy Morrell will be looking for his side to soon rediscover that happy knack of scoring goals when on top in matches.
Nuneaton Town: James Belshaw, Theo Streete, David McNamee (Delroy Gordon 89), Gavin Cowan, Gareth Dean, Daniel Sleath, Adam Walker, James Armson, Andrew Brown, Louis Moult, Wesley York (Connor Taylor 94).
Subs: Jon Adams, Mark Bell, Greg Pearson.
Wrexham: Joslain Mayebi, Steve Tomassen, Leon Clowes, Neil Ashton, Johnny Hunt; Kevin Thornton (Andy Morrell 76), Joe Clarke, Robbie Evans; Andy Bishop, Brett Ormerod, Joe Anyinsah (Adrian Cieslewicz 17).
Subs: Andy Coughlin, Junior Ntame, Jonathan Royle.
Referee: Paul Rees (Avon)
Nuneaton: Walker (45, foul)