Julie Watts, 32, a former psychiatric nurse, was cleared of murder by a Manchester Crown Court jury last September, but convicted of the manslaughter of her 14-month-old baby Abigail, who had a combination of serious birth defects.
Mrs Watts, of Little Hulton, Greater Manchester, who was given an 18- month jail sentence suspended for two years, went to the Court of Appeal in London to tell three judges her conviction was "unsafe".
She hugged her solicitor and sobbed as Lord Justice Swinton Thomas, sitting with Mr Justice Connell and Mr Justice Poole, allowed her appeal.
The court ruled that the trial judge, Mr Justice Sachs, had given the jury inade- quate direction on the issue of manslaughter.
Mrs Watts' daughter Abigail was born with a rare skull deformity, clover leaf syndrome, which left her brain-damaged, deformed, partially sighted, deaf and unable to breathe or feed without help.
The jury at her trial heard that Mrs Watts was constantly at her daughter's bedside, and on one occasion saved her life with emergency resuscitation.
At the end of July 1995, staff at the Royal Manchester Children's Hospital responded to Mrs Watts' cries for help and found that a tracheotomy tube had become detached from Abigail's throat. The child suffered respiratory failure leading to cardiac arrest. Mrs Watts, who has a baby daughter, born in November 1996, and a nine-year-old son, denied interfering with the tube.
After yesterday's appeal verdict she described her ordeal. "This has been the most horrendous two and a half years of my life," she said. "I am very pleased about the outcome today, but I would like more questions asked about the events leading up to her death."
Her solicitor, Kristina Harrison, said: "She is just taking it one step at a time now and I cannot say yet whether she will be claiming any compensation."