Town came away from Dagenham & Redbridge empty handed as Angelo Balanta second half brace sealed the points.
An own goal had given Town the advantage, though the hosts were soon level through Chike Kandi, only for Brendan Kiernan's first goal for his new club to restore the advantage.
Mitch Brundle's header levelled things up before the break, before Balanta struck twice in the second half to send Town to a third defeat in a row.
Simon Weaver made two changes from Tuesday night, with Will Smith and Scott Brown replaced by Ryan Fallowfield and Jack Emmett, who made his 200th appearance for the club.
In the opposing dugout, Peter Taylor made five changes to his Dagenham side, a strong reaction to his side's showing during a midweek 3-0 loss against Boreham Wood.
Taylor's side had the chance to take the lead after five minutes when Warren Burrell was robbed in possession by Balanta, who then fed Kandi, but Town's defender was able to hook the finish off the line after James Belshaw had got something on the attempt.
Two minutes later Town opened the scoring when Joe Leesley's corner ended up in the top corner with Balanta looking to apply the unfortunate final touch.
The lead lasted just seven minutes though as Kandi was again played through on goal, this time by Alex McQueen, and slotted past Belshaw.
McQueen though he had put his side ahead soon after when managing to scramble a long ball past Belshaw and roll into an empty net, though Referee Carl Brook judged the attacker to have handled the ball and the goal was ruled out.
While it could have been 2-1 to the hosts, Town took full advantage of the decision minutes later as Kiernan collected the ball from Jack Muldoon before cutting inside on his left and claiming his first Town goal.
It was level again before the half hour mark though when, Brundle headed home a corner unchallenged, after Belshaw had denied Joan Luque with an impressive save.
Both sides went close to finishing an end to end first half ahead, first when Elliot Justham kept out Muldoon's finish, then when Balanta flashed a header from a corner inches wide of the post in the dying seconds.
The second half started in the same vein as the first ended, with chances for both teams, though Will Wright's chipped finish left a lot to be desired after the full back had stormed forward from defence.
Beck's back post header was kept out the net by an important defensive block, minutes before Kiernan converted Fallowfield's low cross, only to look up and see the linesman's flag raised for offside.
Just like Town had done in the first half, Dagenham took full advantage of the disallowed goal, taking the lead for the first time on the hour mark as Balanta curled past Belshaw.
Sam Jones was introduced, with Town switching to a 3-4-1-2 formation in an effort to find an equaliser, though chances did not follow.
With five minutes to play, Balanta made sure it would be Dagenham who came out on top as he converted Kandi's cross at the back post.
Harrogate Town: Belshaw, Fallowfield, G Smith (Jones 69), Falkingham, Burrell, Emmett, Beck, Leesley (Thomson 61), Kiernan, Mudoon, Hall
Subs not used: Cracknell, Stead, Brown
Goals: Balanta OG 7, Kiernan 24
Dagenham and Redbridge: Justham, Wright, Clark, Croll, Wood (Gordon 66), Brundle, Phipps, McQueen, Balanta (Quigley 87), Luque (Grant 61), Kandi
Subs not used: Robinson, Dobson
Goals: Kandi 14, Brundle 29, Balanta 60, 85
Referee: C Brook
Attendance: 1043 (60 away)