It was substitute Trevor Benjamin who put paid to any hopes the home side might have had when he struck a wonder goal in the 73rd minute.
Clint Easton crossed from the left and although at an acute angle at the near post Benjamin somehow whipped in an unstoppable shot to put the visitors two goals clear.
The game's deadlock had been broken in the 53rd minute when Richard Hope handled and Kris Taylor lashed the ball home, which prevented the Wrexham man being sent off in the 53rd minute.
Danny Williams did give the Bulls a fright in the 77th minute with a storming shot which keeper Wayne Brown tipped over the bar.
Although Neil Roberts missed a chance and placed a header wide in the first half Wrexham, lacked any real penetration up front and had suffered a blow when central defender Steve Evans went off injured in the 15th minute.
Wrexham boss Brian Carey brought on his substitutes to inject some life into his side in the second half, but they were continually stretched, particularly by Theo Robinson and Toumani Diagouraga, who gave Shaun Pejic and Hope a hard time.
Former Wrexham player Graham Turner, now the Hereford boss, must have got great satisfaction at seeing his side maintain their unbeaten record and the fans must have been delighted with both goals, coming at the visitors' end at the Racecourse Ground.