Second best for long periods, the Sulphurites had to do plenty of defending and rode their luck at times, finally recording a long-overdue clean-sheet as strikes from George Thomson and Alex Pattison did the damage at the other end.
The Cumbrians came into the game second-from-bottom of the table and without a win in 11 matches, but could have been in front as early as the eighth minute.
Brad Young glanced a header from a right-wing cross against the upright with Mark Oxley motionless, then Kelvin Mellor nodded over the bar as the ball was recycled and delivered back into the six-yard box.
With Town resorting too often to launching hopeful punts forwards, it was United who continued to look the more likely, Jordan Gibson firing one long-range strike narrowly wide and seeing another pushed wide by Oxley.
It took until the 39th minute for the visitors to create a decent opening, however Jack Muldoon could only direct a tame header straight at Mark Howard from Diamond's delicious left-wing centre.
But, despite having done a decent job of making opponents with absolutely no form to speak of look a decent team for a good chunk of the 45 minutes that had gone before, Harrogate edged ahead just seconds before the interval.
Muldoon found Thomson on the right-hand edge of the Carlisle box, and having got beyond his marker, he drilled a clinical finish across Howard and into the bottom corner.
Undeterred, the hosts were fast out of the traps at the start of the second half and should have got back on terms when Warren Burrell carried the ball out from centre-half but then got caught in possession.
Callum Guy drove into a gaping hole and played Young clean through, however the latter's finish beat both Oxley and the post.
Zach Clough then shot narrowly wide before drawing a good stop out of Town's goalkeeper as the pressure on the away goal was steadily cranked up.
But, having hung in there, Town delivered a killer blow on 78 minutes.
Pattison started and finished a devastating counter-attack, winning possession and driving down the centre of the pitch before calmly slotting home when Howard parried Diamond's strike into his path.
Luke Armstrong then went close to making it 3-0 soon afterwards, forcing Howard into action at his near post as United were forced to throw caution to the wind.
Six minutes of added time afforded the Cumbrians enough time to launch a last-ditch attempt to get themselves back into the contest and Oxley ensured that he finished the evening with a first clean-sheet since late September when he produced a fine reaction save to keep out Corey Whelan's header at point-blank range.
Victory lifts Weaver's men up to sixth in the League Two standings.