Two second half Matt Smith efforts within six minutes send Town home empty handed from thier latest trip to Salford City.
Harrogate had created the best chance of the game up until 20 minutes to go, when Smith capitalised on Mark Oxley being down injured to head into the back of the net.
There was nothing substitute keeper Joe Cracknell could do about Smith's second soon after as the Ammies forward's finish went in off the post to seal the points.
Simon Weaver made one change from last weekend as Lloyd Kerry replaced the injured Jack Muldoon, while Academy striker Finn O'Boyle was named on the bench for the first time.
Meanwhile The Ammies made three changes, including a first start for Luke Bolton, while Ibou Touray and Stephen Kelly returned.
Harrogate created the best chance of the half after 12 minutes of play, Calum Kavanagh playing through strike partner Luke Armstrong, though the former Salford forward could only slide past the post.
It was an battling first half at The Peninsula Stadium, with Lloyd Kerry in the thick of things in the heart of midfield.
Salford struggled to make inroads towards the Town goal, with timely blocks from Nathan Sheron and Warren Burrell ensuring the half ended goalless.
George Thomson almost put Town ahead six minutes after the restart as his left footed volley took a big deflection before rolling inches past the post.
Seconds later Armstrong got on the end of Jack Diamond's cross, only for Tom King to come out and collect the finish.
The contest had sprung into life with Salford racing up the other end and creating their first chance, though a typically brave piece of Mark Oxley goalkeeping denied Luke Bolton.
Thomas-Asante was next to go close as he volleyed second half substitute Mark Beck's headed clearance back towards goal, though it didn't trouble Oxley.
The hosts took the lead with 20 minutes to go when hesitation at the back allowed Thomas-Asante in ahead of Oxley, leaving the Town keeper injured on the floor and unable to stop Smith heading home from a lofted cross.
The incident left Oxley unable to continue, with Joe Cracknell taking his place in goal for the final 17 minutes.
Just five minutes after going ahead, Salford doubled their lead with Smith again the man on the scoresheet, the Ammies forward's acrobatic effort finding it's way in off the post.
Salford had their tails up after the goals and nearly added a third when Donald Love struck sweetly past the top corner.
Armstrong nearly gave the travelling Town fans something to cheer about in the 90th minute, but his strike across goal hit the inside of the post and bounced clear, ensuring Town left empty handed.
Town: Oxley (Cracknell 73), Fallowfield, Smith, Burrell (McArdle 62), Thomson, Kavanagh (Beck 59), Sheron, Pattison, Kerry, Diamond, Armstrong
Subs not used: Austerfield, Ilesanmi, O'Boyle
Salford City: King, Love, Touray, Lowe (Shephard 84), Ndaba, Watson, Kelly, Smith, Bolton (Hunter 85), Thomas-Asante (Henderson 90+3), Vassell
Subs not used: Torrance, Lund, Burgess, Turnbull
Goals: Smith 70, 75
Referee: A Kitchen
Attendance: 1,670 (213 away)