Brady forged ahead, but Lassman was on hand to tap home after a shot from Daniel Alfreds had been parried.
The home side regained the lead, but Team levelled for a second time as the industrious Marks headed home a free-kick from Radstone.
Team stepped up a gear in the second half and went 3-2 up when Kaye headed in another precision delivery from Radstone. It was soon 4-2 as Marks registered his second following a cross from Alfreds.
Brady scored again to make it 4-3, but Team restored their two-goal advantage as the magnificent Lassman capitalsied on a mistake in the Brady defence to coolly slot home.
The visitors sealed the tie with a sixth as another delivery from Alfreds found Madanes who dummied a defender and passes the ball into the goal.
A jubilant Gordon told JC Sport: "It was an absolutely unbelievable performance from every single one of the outfield players today. To a man they were superb and the 6-3 scoreline did not flatter us."
We were up for it from the start, didn’t let Brady play and we were clinical in front of goal. I can’t praise the boys enough and they probably all needed ice-baths after the effort they put in!
"We know we’re in for a tough draw in the semi-finals and I will be ordering the boys to wrap themselves in cotton wool for the next two weeks!"
