The towering Sulphurites frontman broke the deadlock with a cultured finish and Simon Weaver's men never looked back, chalking up a seventh victory in 10 matches as they climbed up to 10th position in the League Two standings.
The home side could not have wished for a better start to proceedings, getting their noses in front almost straight from kick-off.
Beck hung in the air and nodded a bouncing ball forwards for strike partner Josh March, who in turn found Lloyd Kerry on the edge of the box.
Harrogate's veteran midfielder then picked out the unmarked Beck on the right edge of the penalty area and the big centre-forward curled a low strike across Shamal George and inside the far post.
Twelve minutes later, a mammoth Dan Jones throw-in from the left made its way all the way through to Will Smith at the back stick, and only an excellent last-ditch block by a visiting defender denied the hosts a second.
Despite their disastrous start, Colchester eventually began to show some signs of life and Aramide Oteh fired wide from a decent shooting position.
The Essex side came closer still on 22 minutes when Michael Folivi picked the ball up in a similar position on the left side of the Harrogate box and bent a much cleaner strike narrowly the wrong side of James Belshaw's upright.
Ryan Fallowfield was then off target for Town at the other end having raced forward on the overlap from right-back and got himself on the end of George Thomson's nicely-weighted pass.
Weaver's troops continued to look the more likely as the interval approached, but on an extremely tricky pitch, their work in possession wasn't always as tidy as it needed to be.
And, the visitors were very much in the contest as the fourth official indicated that there would be two minutes of stoppage time at the end of the half.
Disaster would however then strike as the away defence switched off having initially dealt with a Thomson free-kick from close to halfway.
The second ball was launched straight back towards the United box, and the away team inexplicably stopped playing, allowing Smith to stroll through on goal unopposed and beat George with ease.
Colchester switched to a 4-4-2 formation for the second period and almost got themselves back in the game within a minute of the re-start, Tommy Smith meeting an inviting left-wing corner inside the six-yard-box and hitting the inside of the post.
The visitors continued to defend in shambolic fashion however, and Thomson's 53rd-minute pass from right to left found Josh McPake unmarked inside the box.
The Glasgow Rangers loanee fooled Junior Tchamadeu with a clever drop of the shoulder, though failed to beat the advancing George and wrap up the points.
McPake would however make amends three minutes later after once again being picked out by Thomson in an almost identical position. This time, he did find a finish, managing to direct a low shot beyond the United custodian.
Town appeared to be cruising at this point, but although much of their play left plenty to be desired, Colchester did have chances to haul themselves back into the contest.
Oteh was denied by an excellent one-one-one block from Belshaw before the Harrogate stopper pulled off an excellent double-save to thwart Tchamadeu's initial effort and then Oteh again on the follow-up.
Colchester continued to engineer some promising situations in the closing stages, and while Town looked very dangerous on the counter-attack, there were to be no more goals before the full-time whistle.
Harrogate Town: Belshaw; Fallowfield, Smith, Burrell, Jones; Thomson, Falkingham, Kerry (Francis 69), McPake (Kiernan 69); March (Muldoon 23), Beck (Martin 80). Unused substitutes: Minter, Lawlor.
Colchester United: George; Eastman, Sowunmi (Pell 46), Smith; Tchamadeu, Chilvers (Cowan-Hall 67), Sarpong-Wierdu, Clampin; Folivi (Brown 67), Harriott, Oteh (Poku 74). Unused substitutes: Coulter, Welch-Hayes, Doherty.
Referee: S Mather (Atherton).