Morrison, who resurrected his career at Birmingham last season, scored from a splendid 14th-minute free-kick and netted an easy second in the 72nd minute at St Andrew's to plunge his former club to their 12th successive home game without a win.
But Rangers, bankrolled to a staggering £65.4million loss in their unsuccessful bid to retain Premier League status last term, made hard work of their return to winning form and may point to the need for a more ruthless streak despite the 2-0 scoreline.
Recent poor form has been a serious set-back to their promotion aspirations when they have lost ground to the two top Championship clubs, Leicester City and Burnley, to the consternation of their popular manager Harry Redknapp.
They were boosted by the return of the influential Joey Barton, and the London club took command very early in the proceedings and should have scored a more conclusive win.
Crisis club Birmingham - who this week saw owner Carson Yeung sentenced to six years in prison for money-laundering by a court in Hong Kong - battled bravely and played with plenty of early attacking energy, only to be thwarted by Rangers' experienced rearguard.
Rangers stamped their authority on the game in the 14th minute after Birmingham's skipper Paul Robinson conceded a needless free-kick on Kevin Doyle and earned the first booking of the match.
It was from the resultant set-piece that Morrison opened the Londoners' account with a high floated shot to the right of goalkeeper Darren Randolph's groping fingers for his first goal for the Championship side since his on-loan move from West Ham.
Birmingham's best chance of an equaliser came three minutes later and it was only a world-class save by Robert Green which enabled Rangers to maintain their advantage.
Emyr Huws, a young player of rich promise, powered in a free-kick which bounced high towards the top far corner of the net only for Green to tip the ball just over the bar.
Huws had another opportunity but he was far too casual and drifted wide instead of shooting from close range as Rangers surprisingly appeared suspect under pressure.
They were much happier on the attack and Clint Hill's header from Barton's 40th-minute free-kick cannoned back off the crossbar.
Over-elaborate play on the part of Rangers was the reason they were unable to increase their slender lead until the 72nd minute.
Jermaine Jenas made progress down the left and stroked a low ball into the middle where the lurking Morrison had ample time to side-foot home his second goal to seal a long overdue Rangers win.