David Gormley was denied by the woodwork from Ciaran Donnelly's corner as Rovers continued to press for the opener at Cliftonhill.
But they made the breakthrough in the 62nd minute when Pollock fired home after Gormley's clever lay-off.
Albion: Gaston, Reid, McGowan, Donnelly, Benton, O'Byrne, Boyle (Stewart 62), Tyrrell, Gormley (McCusker 72), Pollock (Walker 86), Strachaen. Subs Not Used: Ferry, Ewings.
Booked: McGowan, Boyle.
Goals: Pollock 62.
Elgin: Gibson, Dempsie, Inglis, Kaczan, Edwards (Crooks 77), Niven, Gunn (Cameron 83), MacAulay, Frizzel, Nicolson, Tatters. Subs Not Used: Calder, McLeod, Robertson.
Att: 275
Ref: G Hilland
Source: BBC Sport
Source: BBC Sport