Both had denied the charge, but were found guilty in unanimous verdicts at Swansea Crown Court in April.
The court heard that the pair knew the teenager had taken heroin and was showing signs of an overdose, but did not call an ambulance.
Instead they put her in the recovery position in her bed at their terraced home in the Pwll area and then went to watch Emmerdale on TV.
Townsend told the court she believed her daughter would "sleep it off".
During the two-week trial the jury heard that on 2 May last year Carly had bought three bags of heroin.
The prosecution said her half-sister had helped Carly buy the drugs and she and her mother "took a risk" with her life by not seeking medical help.
The jury had been told that Townsend and Evans feared they and Carly would get into trouble.
They found her dead in bed the following morning and called police and paramedics.
Carly lay dying while her family watched television, the court heard
Prosecutor Paul Thomas said they owed Carly a duty of care and their actions amounted to gross negligence.
The defence case was that the pair did not believe Carly was in danger.
Townsend told the jury Carly had been hospitalised twice for heroin overdoses and she had seen her daughter in far worse states than the one she was in on the night she died.
She also told the court that "about 20" of her friends had died through drugs, including her husband, who was Carly's father.
She said her husband had overdosed on the heroin substitute Palfium, while Carly's half-sister had once collapsed after taking heroin and had to be saved by paramedics.
Evans declined to enter the witness box to give evidence on her own behalf.
The court was told that Carly was released from a secure unit in Neath 10 days before her death, and her mother said she did not tell anyone in authority her daughter had taken heroin because she could have been returned to custody.
Sentencing the pair, Mr Justice Lloyd Jones told them they were both only too aware of the symptoms of a heroin overdose.
He also said they knew that there was a drug available that could have immediately reversed the effects of the overdose.
He told Evans and Townsend they could be considered for release on licence after serving half their prison terms.
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