The Iron kicked-off the contest second-from-bottom of the League Two standings, albeit having played a couple of games less than many of their rivals, but with just eight league goals to their name in 12 outings.
They would however go on to win at a canter, opening up their hosts at will while outplaying them in all areas of the pitch, and while Harrogate's manager revealed that he felt "let down" by his team's performance, he refused to be overly critical.
"We were dealt a harsh lesson tonight. We deservedly lost by that scoreline. In all departments Scunthorpe were better than us," he said.
"We have to be stronger and have a more resilient mindset. Even five minutes in, there looked to be resigned looks on people's faces.
"If players are really honest tonight, probably only two or three shone and one of them was Jack Muldoon, because he scored. We didn't have any real concerted pressure. We looked like we had run out of juice.
"But, we've got to stay patient and back the players. We've come into this season on the back of a fairy-tale and you can't expect that just to continue
"I've got to get the balance right with the lads, because whilst you feel let down, you have to remember the shift that they have put in for weeks and weeks. There will be bumps in the road and we have to forgive and move on quickly."
Scunthorpe dominated the opening exchanges, almost taking the lead on three minutes when Manny Onariase headed into the turf and over the bar from Abo Eisa’s excellent left-wing cross.
The pair combined again just after the quarter-hour-mark and this time Eisa’s inviting delivery from the same flank was adjudged by the officials to have been finished off at the back post by the big centre-half, despite the best efforts of James Belshaw.
Eisa then saw an effort deflected narrowly the wrong side of the upright, while only a fine Warren Burrell header underneath his own cross-bar prevented Ryan Loft from making it 2-0 from a Mason O’Malley centre.
Having found themselves thoroughly second best for half an hour, Town eventually weathered the storm and drew level 10 minutes before half-time.
George Thomson delivered a free-kick from left to right which Mark Beck nodded back across goal for Jack Muldoon to smash home in emphatic style.
With that goal, the momentum seemed to be shifting, only for Harrogate to then gift their visitors a second of the night.
Auxiliary right-back Connor Kirby twice lost the ball inside his own half, allowing John McAtee to slide Eisa through on goal for a simple finish past Belshaw.
Weaver shuffled his pack at the interval and his side began the second period better than they had the first. Indeed, they looked very much in the game until the 62nd minute, when Calvin Miller's heavy touch in the left-back position set the visitors away down the right on a counter-attack.
Alex Gilliead's attempted cross the ball into the box then struck the arm of Muldoon, prompting referee Paul Howard to award a harsh penalty kick, which was confidently dispatched by Eisa.
The game was effectively over as a contest from this point onwards and, as was the case in Saturday's 4-0 FA Cup loss to Blackpool, Town started to fall apart.
United's fourth of the evening arrived in the 73rd minute, Miller stopping after he thought the ball had run out of play and enabling Gilliead to run clear down the right and pick out Loft for the easiest of close-range finishes.
A good stop by Belshaw prevented substitute Jake Taylor from making it 5-1, though the Harrogate keeper would make a mess of clearing the ball inside his own box minutes later, leaving Aaron Jarvis with an empty net to shoot into.
Connor Hall's neat bit of control and clinical finish in stoppage-time would ensure that the hosts had the final say, though that late consolation will do little to ease the pain of a galling defeat.
Harrogate: Belshaw; Kirby (Kiernan 46), Lawlor, Hall, Burrell; Thomson, Falkingham, Kerry (Martin 68), Miller; Muldoon, Beck. Unused substitutes: Cracknell, Stead.
Scunthorpe: Howard; Clarke (Rowe 78), Onariase, McGahey, O'Malley; Gilliead, Beestin, Spence, Eisa, McAtee (Taylor 75), Loft (Jarvis 75). Unused substitutes: Watson, Bedeau, Green, Hallam.
Referee: Paul Howard (London).