But the Lancashire side, in their first-ever campaign in the Vase, dominated the rest of the first half, with Mark Wane wasting a good chance and Paterson seeing his brilliant volley hit the crossbar and bounce on the line.
After the break, Kirkham continued to dominate although Bradley Hough had a chance to seal the tie for Eastern Counties Premier Division side Lowestoft, but fired over.
Paterson, Wane and Paul Eastwood all missed chances in a desperate goalmouth scramble and it looked likely to be Lowestoft's day.
However, in the 79th minute, manager Mick Fuller brought on Walwyn, who had scored the goal that sealed their place at Wembley, and the decision changed the game.
Walwyn levelled five minutes later after controlling Paterson's ball and slamming the ball past Andy Reynolds.
And the A-level student sealed the Vase for the 10th-tier side when Paterson unselfishly set him up, and he could not miss.
Walwyn, son of former Blackpool striker Keith, told BBC Radio Lancashire: "It was absolutely brilliant.
"There isn't a better feeling. It's unbelievable. We'll be taking the trophy back to Wesham and that's the main thing."
Kirkham & Wesham:
Summerfield, Jackson (Walwyn 79), Keefe (Allen 55), Thompson, Shaw, Eastwood, Clark, Blackwell, Wane, Paterson (Sheppard 90), Smith.
Subs not used: Moffatt, Abbott.
Booked:
Smith.
Goals:
Walwyn 84, 90.
Lowestoft Town:
Reynolds, Poppy, Potter, Woodrow, Saunders, Plaskett (McGee 79), Godbold, Darren Cockrill (Dale Cockrill 46), Stock, Hough, King (Hunn 55).
Subs not used: McKenna, Rix.
Booked:
Woodrow.
Goal:
Thompson og 10.
Att:
19,537
Ref:
Andy D'Urso (Essex).
