There was little between the sides during Tuesday evening's contest, though the Red Devils kept their own error-count down and were ruthless enough in the attacking third to take advantage of some sloppiness from the home players.
The visitors broke the deadlock three minutes into the second half when Town opted to check back rather than press forwards on the counter-attack, Josh Falkingham then losing possession to Aramide Oteh, who was able to run from inside his own half and slot beyond Mark Oxley.
Brahima Diarra capped an impressive performance by getting Harrogate back on terms just after the hour-mark, though Warren Burrell was then caught dithering by Tom Nichols, who was able to cross from the right to leave Nick Tsaroulla with a 79th-minute tap-in.
More ragged defending then presented Nichols with a sight of goal just over 20 yards out, and Crawley's stand-out performer on the night ended the game as a contest with a cultured curling finish that kissed the upright on its way into the net.
"It's frustrating. It was a tight game but Crawley deserved the win because we made individual errors, we didn't do enough in the final third and, overall, we didn't play well enough," Weaver reflected.
"At the back, it was kamikaze stuff. Their goals have come from nothing. We've been negative for their first goal and taken the sting out of our own attack when Lewis Page was overlapping from full-back. Then we've given the ball away and nobody has brought their lad [Oteh] down as he's running away. It's mad.
"That one was a culmination of errors, but as much as we'll blame the back-line for some of the mistakes tonight, to concede a goal through being negative, it's not us. Some of the decision-making beggars belief.
"The second goal is an individual error again and it's just not good enough for the standard. We've got to deal with that situation better and it's something that has happened too many times. There was no reason why we couldn't have gone on and won it at 1-1, but then you get these mad moments.
"In this league, it's so much about just being steady at the back and streetwise. We've got to stay in games because we do have individuals who can do the damage going forwards, but you've got to give those lads a chance."
Tuesday's defeat sees Harrogate slip two places in the League Two standings to 13th position.