The Latics had gone into the game defending one of the best home records in the division, but Morrison's goal right on half-time – following Adams' opener – gave Blues valuable breathing space.
And Maghoma made it three just after the hour mark, with Wigan chasing shadows by this point and slipping further down the table after a promising start.
Wigan started as the stronger side and were almost in front inside five minutes.
Gary Roberts went past four defenders down the left wing and his cross was just about cleared before James Vaughan could slot home.
But as they continued to knock at the door, Wigan were rocked on their heels by a goal of stunning simplicity from Birmingham.
Adams fed Lukas Jutkiewicz and took the return pass before slotting past an exposed Christian Walton.
Wigan thought they had been given a way back into the game when Cedric Kipre appeared to have been tripped inside the penalty area, but referee Ross Joyce was unimpressed and waved play on.
Roberts and Kal Naimsith linked up well again down the Wigan left, with the latter's delivery being cut out before Vaughan could pounce.
Birmingham, though, remained a real threat and Adams almost took advantage of a total breakdown in communication between Reece James and Dan Burn, who were indebted to Sam Morsy for coming across to snuff out the danger.
The respite was only temporary, however, with the resulting corner being flicked on at the near post and Morrison slotting home, totally unmarked, from close range.
Wigan's attempts at a response at the start of the second period were hampered with Vaughan limping off just two minutes after the restart, although that at least allowed them to get Will Grigg on to the field.
Outstanding defending from Morrison denied Burn what he thought was going to be a tap-in, before Josh Windass somehow headed wastefully wide from six yards.
And any lingering hopes Wigan had of getting anything out of the game were extinguished on 61 minutes, when Jutkiewicz's header goalwards was steered over the line by Maghoma.
Wigan came close to a consolation when Kipre headed against the bar from a James free-kick, but the visitors looked by far the likelier scorers had another goal arrived, with former Wigan man Omar Bogle going close on a couple of occasions after coming off the bench.