The home side were in control throughout this game but could never really assert their authority over the Belfast side in terms of goals and it was left to the recently retired international captain Rachel Kohler to force the issue with a tremendous opening goal late in the first half.
They settled it with a second from Marissa Ahern midway through the second half, but afterwards coach Ivan Bateman was more than a little relieved that his side's recent problems finding the net had not posed more problems.
"It is very difficult when you are in control of a game but just cannot break your opponents down," he said afterwards. "It was certainly not as fluid as I would have liked, but I was impressed by our attitude to the game because we knew Knock would not give anything to us too easily."
"On paper we should have won, but we came into the match very focused on what needed to be done and we stuck at it," he added.
However, the failure of his side to score from any of the eleven short corners they forced during the course of the match, is certainly a worry for the coach and while he was delighted with the two goals from open play, he was clearly frustrated by his side's inability to take their set piece chances.
"Our play from short corners was not great and I am disappointed by that, but it is something we will continue to work on and hopefully improve.
"We did have possession for large amounts of the game, but Knock were very organised and very determined and they defended in numbers, but we stuck to our task and we got the result we deserved in the end."
Part of Harlequins' problem was that they over-elaborated their corner routines, often bringing as many as five or six moves into any one set piece, and they suffered as a result.
Kohler, who retired from international hockey after last year's European Championships, remains 'Quins most effective player by some margin and Bateman was quick to praise the efforts of his captain, especially as the first goal was completely down to her individual brilliance.
Thirty-three minutes into the game, Kohler received a pass outside the circle and with a wall of Knock players in front of her, the options seemed limited, but she simply put her head down, dribbled around several defenders and, once inside the circle, lashed an unstoppable shot into the roof of the visitors' net.
It was class play from a class act.
Quins' other retired international Karen Bateman was also in the thick of the first half action and, although she was playing from a relatively unfamiliar midfield position, the former Irish striker created perhaps the best chances of the period, flashing one reverse stick shot just wide and then seeing another venomous bullet cleared off the line by Knock skipper Laura Edgar.
Bateman continued the pressure in the second half, shooting narrowly wide from yet another Quins' short corner but, as the home side increased the pressure on Knock, they were unable to increase their lead.
Kohler had a shot taken off the line by Marj Quinlan and several other increasingly simplified short corner opportunities went begging before Marissa Ahern more or less settled the issue with a fine second goal 18 minutes in after some excellent build-up work by Carrie O'Callaghan.
So, Quins now progress in the competition, but they will know that against tougher opponents, they will have to make better use of their possession, otherwise it might cost them dearly.
CORK HARLEQUINS: O. McCarthy, J Hyland, N Kearney, S Canning, E Dillon, K Bateman, R Kohler, J Barry, M Ahern, J Chapple, J Dillon. Rolling subs: C O'Callaghan, J O'Halloran, H Costello, A O'Farrell.
KNOCK: N. Cannock, E. Dunn, L. Place, B. Wight, L. Edgar, M Quinlan, G Thompson, D Millar, K Crawford, J Doak, S Mills. Rolling subs: V O'Neill, S Edgar, J Carlisle.
Umpires: C Hickey (Connacht) and P Hales (Leinster).