Birmingham carved out the better openings and should have been ahead at the interval with better finishing and though the introduction of David Bellion early in the second half gave the Black Cats a much-needed injection of pace, a goalless draw looked the likely outcome.
Third choice goalkeeper Jurgen Macho, given a vote of confidence on the strength of his heroics against Liverpool despite the arrival of Mart Poom from Derby County, saved well from Paul Devlin and Morrison and only a last-ditch tackle by Stephen Wright denied Stan Lazaridis a clear run on goal.
Aliou Cisse blazed wide with the goal at his mercy and the best Sunderland could muster was a couple of 25-yard efforts from Michael Proctor with the more experienced Kevin Phillips and Tore Andre Flo given few chances to impress.
Robbie Savage, always in the thick of the action again, showed his displeasure when substituted on the hour just two minutes after being booked for a challenge on Gavin McCann.
But manager Steve Bruce played down the incident, claiming his side had three midfield players booked and he couldn't afford to finish with ten men. "He did not want to come off but it's over now and I am paid to make the decisions,'' he said.
"It's awfully cruel to lose a game to a goal in the last minute but I thought we were the better team on the day and deserved to win"It's vital you give yourself a platform to work on by not conceding and we have worked hard at keeping clean sheets. We've got to be realistic if we want to stay in the Premiership because there is a hard winter ahead.''
Only the woodwork prevented an attempted clearance from Olivier Tebily striking substitute Damien Johnson and giving Sunderland an 86th minute lead and the match-winning goal was also blessed with good fortune.
Michael Gray was caught in possession and when Jody Craddock's clearance struck Morrison, he went clear to slam the ball home to the delight of the Birmingham supporters behind the goal.
Sunderland boss Howard Wilkinson expressed his disappointment but hopes his players have learned a harsh lesson.
He said: "The most important thing today is we don't allow our overall performances to be allowed to be washed away and down the pan.
"We have got to learn and move on. Performances have been improving but we have to get into the mood not to let mistakes happen. We must not think we have come a long way in a short time.''