A lob by Mark Kinsella was punched cleared by keeper Neil Sullivan and the ball fell perfectly for Morrison to shoot home from the edge of the box for his fourth international goal.
Paul Devlin appeared for Scotland as a second half substitute and made a number of fine runs down the right wing, earning him the man of the match accolade.
Elsewhere, Robbie Savage played a part in Wales' draw with Bosnia Herzegovina at the Millennium Stadium, Cardiff, setting up John Hartson's equaliser on 66 minutes to bring the scores level at 2-2.