Nelson dug in for an hour with 10 men on Tuesday night to claim a welcome point at Prestwich Heys.
Steve Cunningham’s men went ahead through Gareth Hill on 14 minutes, but the hosts levelled matters nine minutes later through Lee Bruce.
There was a further blow for the Admirals as Charlie Lloyd was sent off on the half hour.
But Nelson, with former Padiham and Colne man Kenny Taylor making his debut, reorganised and put in a superb shift to grind out a point, and were unlucky not to snatch all three with the chances they had.
That came on the back of Saturday’s 3-1 win at Little Wembley against St Martins in the First Division Cup first round.
Nelson again had to do it the hard way, as they fell behind to a Jordan Davies goal just before the half hour mark.
But home debutant Nathan Webb equalised right on half-time, and the Blues came out to boss the second half and progress in the competition.
Burnley FC second year scholar William Harris, signed on a work experience loan the day before, picked out James Wolfenden with an incisive pass, and his cross was slotted in by Jake Lloyd just after the hour.
Harris himself sealed victory on his debut with the third goal 12 minutes from time.
The Admirals turn their attentions to the Buildbase FA Vase tomorrow, and their second qualifying round tie with Tow Law Town, kick-off 3 p.m.
Town ply their trade in the Northern League Division Two, and were Vase finalists in 1998.