The 46-year-old mother, who cannot be named for legal reasons, had been jailed for two years after she entered the UK on a fake passport in 2005 and then deported.
Last year, an immigration judge upheld her appeal to return to be with her son, who lives with his British father, but that order was challenged by UK Home Secretary Theresa May.
Lord Justice Underhill, who headed the appeal panel, said May should not fear that the decision would open the floodgates to similar appeals, saying each case would "turn on its own facts".
According to reports, the woman first arrived in the UK in 2002 on a "visitor visa" and became involved in a conspiracy to "facilitate bogus marriages".
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It is also believed that she entered into a bogus marriage and was given an extension of her leave to remain in the UK as a result. She was arrested and charged in 2003 but had then fled to India, Asian Image reported.
In 2006, she gave birth to her son and in 2007 was given indefinite leave to remain -- under her false identity.
Shortly after the birth, her true identity was discovered and in 2008 she was given a 12-month jail term after being convicted of obtaining leave to enter the UK by deception, plus an additional 12-month jail term for the 2003 bogus marriage offences.
In 2009 she was deported while her husband stayed in Britain. Initially, her son spent some time in India with her and some time in Britain with his father.
Her lawyers hadsuggested that rights to family life enshrined in Article 8 of the European Convention on Human Rights were being undermined.
Appeal judges analysed all arguments at a hearing in London in July and announced their decision to allow her re-entry this week.