Linlithgow found themselves reduced to ten men in the fourth minute when Jamie MacKenzie was red-carded for a foul on Graeme Dailly.
Ten minutes from half-time, numerical parity was restored when Roddy MacLennan ran the full length of the park before being brought down by Panmure keeper Duncan MacPherson who was dismissed. Josh Perera took over the goalkeeper gloves but was powerless to prevent Tommy Coyne netting the resulting penalty.
Both sides hit the woodwork after the break, Brian Clark for Carnoustie and substitute Gordon Herd for Rose.
The points were sealed with 15 minutes remaining when Herd was brought down in the box by John Young and Coyne dispatched his second spot-kick of the game past Perera. Panmure came close when Dailly’s header hit the post, but in the end Linlithgow ran out reasonably comfortable winners.
Linlithgow Rose: Hay, Gibson, Dunn, MacKenzie, Ovenstone, Shirra, Ruari MacLennan, Nelson, Strickland (Herd 61 mins), Coyne (Smith 87 mins), Roddy MacLennan (McArthur 61 mins).
Carnoustie: MacPherson, Narey (Perera 36 mins), Ferguson (Neave 74 mins), Millar, Young, Roberts, Scott, Robertson, Dailly, Scott (McIlravey 46 mins), Clark.