Molloy (centre) and Redman (right) scored Brechin's goals
Cowdenbeath were relegated to Division Two as Brechin City progressed to the First Division play-off final.
The semi-final first leg ended 2-2 and Brechin moved ahead on aggregate when James Redman fired home from six yards out.
Craig Molloy, who earlier hit the bar, sealed victory with another close-range effort six minutes from the end.
Beath threatened through Steven Crawford and Mark Ramsay but could not find the net.
Brechin City will play Ayr United in the two-legged final.
Hay, Baxter (Coult 7), Armstrong, O'Brien, Linton, Robertson, Ramsay, Cameron, Makel, Crawford, Stewart, Coult (McKenzie 50). Subs Not Used: Wilson, Winter, Byren.
Nelson, Cook, McLauchlan (White 88), Moyes, McBain, McKenna, Molloy, Redman, Kirkpatrick (Janczyk 86), McAllister, Megginson (Fusco 19). Subs Not Used: Scott, Archdeacon.
Redman 78, Molloy 84.