The home made a bright start and could have gone in front when Scott Chaplain laid the ball off for Jamie Doyle whose long-range effort was tipped over the bar by William McCulloch.
From the resulting Doyle corner Albion took the lead as Ciaran Donnelly rose above the defence to powerfully head the ball home.
Albion doubled their lead on 24 minutes when Gordon Lennon threaded the ball through to Chaplain who fired into the net through McCulloch's legs.
However, the home side's joy was short-lived as four goals came in a devastating ten minute spell either side of half-time.
The visitors first came on 37 minutes when Lennon turned the ball into his own net following a McBride corner.
Then just before the break Kevin Nicoll fouled David Templeton just inside the box and up stepped McBride to send Jamie Ewings the wrong way from the spot.
Stenhousemuir took the lead just 30 seconds into the second half as Templeton headed home following a McBride cross.
McBride then got his second and his side's fourth a minute later when he neatly chipped Ewings from the edge of the box.
The Warriors then rounded off the scoring late on when Gareth Hutchison flicked home following a Gordon Connelly cross.