Pat Clarke produced a five-star performance to capitalise on some calamitous Stranraer defending.
Clarke got the first of his five goals after 13 seconds with a low shot, his second a minute later and completed his hat-trick inside 10 minutes.
Pat Scullion added a fourth when he rifled a shot past Black in the 16th minute. Stranraer replied with a Michael Moore goal in 31 minutes.
But it was Clarke's day and he added two second half goals.
Stranraer: Black, McKinstry, McAlpine, Ramsay, Wilson (Sharp 7), Walker, Brian McPhee, Janczyk (McMullan 73), Moore, Hamilton, McGrillen (Mullen 51). Subs Not Used: Snowdon, Allan Ferguson.
Booked: Hamilton, Ramsay.
Goals: Moore 31. Cowdenbeath: Hay, Baxter (Guy 10), Ellis, Armstrong, Hill, Lennon, Clarke, Patrick Scullion, Buchanan, McBride (Ramsey 59), Fotheringham (Bryan 83). Subs Not Used: Dalziel, Allison.
Goals: Clarke 1, 2, 10, Patrick Scullion 16, Clarke 69, 90.
Att: 282 Ref: S O'Reilly