The appeal judge was critical of the original trial judge for sending Mrs Smith to prison. She was a "hard-working, good mother and has been a good wife," he said.
He added that she had never committed an offence and the trial judge should have paid regard to the fact that Mr Smith was the author of his own misfortunes.
"We think the learned judge took a far too restrictive view of this attack," said Lord Justice Bedlam.
Outside court Mrs Smith, 29, a diminutive figure in a black suit, sobbed and clutched a photo of her son as she was hustled out of the back entrance by representatives from a tabloid newspaper.
In a statement issued by the paper last night, Mrs Smith thanked the public and media who supported her in her fight for justice: "I am obviously delighted at the court's decision today." she said.
"But I have been through a terrible ordeal and now just want to be reunited with my children."
She had cried throughout the hearing and collapsed in the dock and had to be carried from the courtroom after hearing the verdict. She had served just seven days of the nine-month sentence and returned to her home in Manchester last night to be reunited with her children.
She was sent to prison by Judge Peter Lakin at Manchester Crown Court last Friday when she admitted assaulting her best friend, Francine French, whom she caught having an affair with her estranged husband, Jeffrey.
The severity of the sentence on a woman with no previous convictions sparked a public outcry and several campaigns for her release.
Replacing her sentence with a year's probation yesterday, Lord Justice Bedlam said that the offence did not merit a custodial sentence and said that Judge Lakin, should have considered what jail would mean for the "caring mother" and her three children.
Describing the background to the case, Nick Clarke, representing Mrs Smith, said that her marriage had collapsed earlier this year and although the couple had a close relationship they were living at different addresses.
The pair were childhood sweethearts who had "enjoyed a very long and happy" marriage during which they had four children, Emma, 11, Jeffrey, nine, Jonathan, seven, and Andrew, who died from a brain haemorrhage when he was nine months old.
Mr Clarke said that "things had come to a head" in August, when Mr Smith made love to his estranged wife and returned to his brother's home, where he was staying. When Mrs Smith went round to the house the next morning she discovered he had stayed overnight with Mrs French, the wife of her former next-door neighbour, who had become her best friend during the split with her husband.
"She wanted to confront them with their betrayal and went to her brother- in-law's house and went into the bedroom, where Mrs French was drying her hair, and wearing her husband's T-shirt." Her husband then emerged from the shower wearing boxer shorts. "Mrs French's reaction she took as a smile or smirk in a mocking manner and she struck out with a shoe she was carrying."
The heel of the stiletto shoe caused two wounds, which each needed a stitch. Mrs Smith suffered more serious injuries in the ensuing fight, including a fractured wrist, strained neck and bruises on her body and face.
Calling for an "act of mercy" from the Court of Appeal, Mr Clarke said that the mother of three had been severely traumatised by the jail sentence and had to undergo heavy sedation in the hospital wing at Risley Prison, Cheshire, where she had been held for the past week.
"She believes the sentence has destroyed her life and parted her from her children and the children are very upset by the removal of their mother ...Whilst the mother was away, the two younger children were removed from their school by their father against their wishes." He said all three children were now back with their maternal grandparents.
Stephen Shaw, director of the Prison Reform Trust, said later: "We are delighted at the outcome. It is a victory for common sense, a victory for justice, a victory for families and a bit of good news in the run up to Christmas."Reuse content