Celtic, who are in the league below Aspatria, were fired to victory by Robert Fowler and Todd Stainton, while Darryl Creighton notched for Aspatria.
In the other quarter final played at the weekend, Wigton Harriers and Netherhall fought out a goalless draw after 120 minutes, with Harriers holding their nerve to progress 4-3 on penalties.
In the Premier Division, leaders Workington Athletic extended their lead at the top with a comfortable 8-0 win at home to Carlisle City thanks to goals for Tony Berwick, a brace for Stu Gray and one each for Gareth Brunton and Mac Sharp.
The game between Whitehaven Miners and Silloth was postponed due to a waterlogged pitch.
Unisun made their longest trip of the season away at Gosforth in Division One, but came away empty handed, going down 8-1.
An Owen Woodburn hat-trick and a brace from Jack Denwood were added to by Rhys Singleton, Ryan Gray and Greg Bedford, with Knott getting Unisun’s consolation.
The Bransty Rangers and Windscale matches were postponed due to bad weather.
The second round of the Benevolent Cup saw another Division One side come out on top over a top flight team, with Borough going through 3-1 on the road at Cockermouth.
The visitors’ goals came from Andrew Marshalsea, Andrew Bezsusko and Liam McCulloch, with Brett McMillan on target for Cockermouth.
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