The Sulphurites conceded within 60 seconds of kick-off, and despite creating plenty of decent opportunities to get themselves back into the contest, failed to do so.
Saturday's loss was Simon Weaver's team's third in four matches and sees them drop to 13th in table, leaving them nine points shy of the top-seven.
Harrogate managed to score in the first very minute of their previous home outing - against Colchester United - but on this occasion they conspired to concede in extremely soft fashion almost straight from kick-off.
The Shrimps attacked down their left and Simon Power failed to get enough on the ball as he attempted to intercept Lewis Gibson's pass on the edge of his own box, providing Carlos Mendes-Gomes with a clear sight of James Belshaw's goal.
The Spaniard's near-post blast was deflected beyond the Town stopper and Weaver's men were left facing an uphill task.
Things looked as if they were going to get even worse for the hosts on 13 minutes when Cole Stockton's inch-perfect through-ball played John O'Sullivan in behind, but despite the Morecambe attacker having plenty of time to find a finish, he was denied by a superb, sprawling block by the onrushing Belshaw.
The danger was not over, however, and as Harrogate failed to clear their lines, Mendes-Gomes unleashed a thunderous strike from distance which crashed against the upright.
Belshaw had to come to his team's rescue once again four minutes later, doing brilliantly to stretch and claw away Stockton's goal-bound lob after Will Smith's hesitancy allowed the Shrimps' number nine in on goal.
What was most worrying from a Town perspective was that their visitors didn't look to have even got out of second gear by this point, though the home team did eventually begin to feel their way into the match.
Simon Power did very well to deliver a first-time cross from close to the right-hand byline and Aaron Martin climbed to good effect, but nodded over at the back post.
And, on the stroke of half-time an even better opportunity presented itself to Martin, though he could only direct a free header from George Thomson's free-kick wide of the mark.
Town began the second period in much brighter fashion and a third headed chance presented itself to Martin on the hour-mark, however he again failed to even hit the target from Dan Jones' long throw-in.
Another monster Jones throw was then completely missed by Shrimps goalkeeper Kyle Letheren, but nobody in a yellow shirt was on hand to apply a finishing touch at the back stick.
At the other end, Mendes-Gomes’ low cross from the left reached O’Sullivan at the far post, though he could only find the side-netting from a narrow angle.
With 75 minutes on the clock, the visitors were reduced to 10 men, Nathaniel Knight-Percival receiving a second booking for handling a ball over the top that he seemed to have misjudged.
Moments later, a Thomson corner from the right was headed against the post by a Town head, the hosts then failing to force the loose ball over the line during an almighty scramble inside the Morecambe six-yard-box.
Next, substitute Mark Beck rose highest to nod a Thomson corner from the opposite side over the cross-bar, but despite their numerical advantage, that was about as close as the Sulphurites were to come during a disappointing final quarter-of-an-hour.
The Shrimps kept nine men behind the ball and defended their penalty area resolutely, ensuring that for the fifth time this season, Harrogate found themselves on the wrong end of a 1-0 scoreline at Wetherby Road.
Harrogate Town: Belshaw; Fallowfield, Smith, Hall, Jones; Power, Thomson, Falkingham, McPake (Kiernan 87); Martin (Beck 75), Muldoon. Unused substitutes: Minter, Burrell, Francis, Williams.
Morecambe: Letheren; Mellor, Knight-Percival, Davis, Gibson; Wildig, Kenyon, Diagouraga; O'Sullivan, Stockton (Cooney 79), Mendes-Gomes (McAlinden 82). Unused substitutes: Halstead, Pringle, Denny, Price.
Referee: J Smith (Lincolnshire).