Lancers manager Martin Gander said: "It was men against boys. I can have no complaints, because they are an outstanding team.
"They showed their class and there was nothing we could do to stop their threat.
"Although I'm obviously dissapointed, 5-1 didn't flatter them and they're in a league of their own. Congratulations to Peacehaven because they fully deserved it."
Peacehaven started brightly and went ahead with their first attack of the game on 10 minutes when Wes Millis headed home Callum Saunders' cross after static defending.
Five minutes later, Lancers were level when Tony Miles thumped home a header from Darren Boswell's corner.
However, parity lasted only seven minutes. Tom Levitt received Ben Sweatman's pass, beat Luke McCabe and Dan Ford, and calmly slotted home from 15 yards.
Peacehaven went 3-1 up in the 25th minute. Burton's cross was met by Levitt, who, unmarked, headed home from 10 yards.
Lancers spurned a glorious chance to pull one back in the 36th minute when Boswell blazed over from six yards after Dan Griffin's free kick was blocked.
The second half was a damage limitation exercise for Lancers with the game seemingly beyond them, and Green had to be at his best when he denied Haven a fourth from Sweatman's drive.
Peacehaven did make it 4-1 midway through the half, when Craig Bunch ran through and slotted home after a superb, flowing, six-man move.
Lancing, to their credit, never gave up, and were unlucky not to pull a goal back when Griffin's cross only needed a touch but evaded everyone.
Will Berry was then denied by Peacehaven keeper Lee Baker, before it was Green's turn to be called into the action, and he denied Haven substitute Richie Watton.
With Lancers praying for the final whistle, the league leaders compounded their misery with the final goal eight minutes from time.
Levitt's shot was stopped by Green, Burton's follow-up effort was also stopped, but the ball broke for Watton, who tapped home from three yards to make it 5-1.
Peacehaven now face Seaford in the final on Good Friday.
LANCING: Green; Turley-George, McCabe, Ford, Miles; Boswell, A.Hunt, S.Hunt, Berry; Georgiou, Griffin. Subs: Gurney (Turley-George 55), Churchill, Burton (Boswell, S.Hunt 70), Gander, Spragg.
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