Top scorer Scott Bakkor gave the hosts a lead 12 minutes in but it was in the 58th minute when Alex Low was shown a second yellow card while conceding a penalty that the tie firmly swung in the Blues favour.
Bakkor struck the bar with the resulting spot kick, although the ten-men of Railway couldn’t prevent Sefton Gonzales twice adding to the final scoreline.
Lee Ashforth named the same starting XI that had secured points against Scarborough and Brighouse Town in their previous two fixtures.
And it was Railway who had the first sight of goal as Dan Thirkell’s long throw fell to Jack Stockdill, although the midfielder’s snapshot was denied by the knees of Benjamin Woodhead.
Despite the visitors encouraging start it was Clitheroe who took the lead when a cross-field ball found Bakkor on the right wing to fire home his ninth league goal of the season.
The visitors started the second period brightly, as they had the first, with Fatlum Ibrahimi sending a shot into the arms of the ‘keeper.
Just moments after Mayers had spurned a golden opportunity heading into the arms of Goodwin, Clitheroe were awarded a penalty when Low brought down Harries.
The centre back was quickly shown a second yellow having been booked just minutes earlier, although Bakkor stepped up to take the spot kick and rattled the cross bar, handing Railway a lifeline.
Gonzales did get on the scoresheet three minutes later when he capitalised on some hesitation from Goodwin nipping in to take the ball and rounding the Railway stopper to tap into an empty net.
Railway did come close to pulling one back when Tom Owen’s powerful header from Lawrance Hunter’s corner was well held by Woodhead, although Goodwin made a more impressive save at the other end just seconds later as he sprung up to tip Michael Hampson’s shot over the bar.
Gonzales then grabbed his second of the game and put the result beyond doubt in stoppage time when he got on the end of a deep left wing cross and directed his header into the opposite corner.
Clitheroe 3-0 Harrogate Railway
Harrogate Railway: Goodwin, Wood, Hunter, Low, Stockdill, Horne, Sharrocks (Clamp 61), Thirkell (Pells 71), Owen, Worrall (Barrett 60), Ibrahimi
Sent off: Low
Clitheroe: Woodhead, Benjamin, Walker, Bonaminio (Barski 37), Brady (Heywood 48), Dent (Hampson 45), Bakkor, Lynch, Gonzales, Harries, Myers
Goals: Bakkor 12, Gonzales 68, 92