Paul Tosh's long-range strike put the visitors ahead 13 minutes before the half-time interval.
McNeil saved efforts from Michael Moore either side of Steven Tweed's volley for Montrose's second on 66 minutes and Noble struck the woodwork late on.
Stranraer: David Mitchell, Glen Mitchell (Moore 55), Bouadji, Henderson (Agostini 69), Sharp, Agnew, Nicoll, Daniel Mitchell, Noble, One, McColm (McManus 78). Subs Not Used: McKillop, Montgomerie.
Montrose: McNeil, McNalley, Crighton, Tweed, Cambell, Milligan, Hegarty, Davidson, Sinclair, Tosh, Tomana (Tresly 85). Subs Not Used: Coutts, Andrew Anderson, Arbuckle.
Booked: Sinclair, Hegarty, McNalley.
Goals: Tosh 32, Tweed 66.
Att: 225
Ref: T Robertson
Source: BBC Sport
Source: BBC Sport