Kimberly Quinn had claimed her physical and mental health were at "significant risk" after Mr Blunkett applied for a contact order over the boy, known as "A" for legal reasons.
But a High Court judge dismissed Mrs Quinn's call for a delay and allowed the case to go ahead.
It emerged that Mr Blunkett spent more than two hours in a private hearing at Court 47 of the Royal Courts of Justice on Thursday the day of Chancellor Gordon Brown's pre-budget statement.
Mr Blunkett did not attend yesterday's hearing but said in a statement: "I'm naturally relieved at today's judgment so I can continue my attempts to gain access to my son.
"I have never wanted anything about my private life and (A's) paternity to be in the public domain and would never have gone to the courts if there were another way of getting informal access to him.
"I still hope this may be possible as I have not seen (A) since August."
Prime Minister Tony Blair's official spokesman said the premier remained fully confident that Mr Blunkett could continue doing his demanding job.
"You simply have to look at what David Blunkett has been doing during the past 10 days in setting out the vision contained in the Queen's Speech, in following that vision through in media appearances and in his work at Cabinet and in his department," the spokesman said.
Lawyers for Mrs Quinn, the publisher of right-wing weekly The Spectator, and her Irish husband Stephen, managing director of Vogue magazine, had said she was unable to participate in the case until April because she is seven months pregnant.
She was unable to give instructions to her legal team and was at "serious risk to her physical and mental health," her lawyers said.
But Mr Justice Ryder concluded: "Mrs Quinn was not incapacitated from giving instructions and was able to take a good part in these proceedings until days, if not hours, before the hearing."
In particular, said the judge, she gave firm instructions in relation to paternity of A, whom she denies is Mr Blunkett's.
Any delay in proceedings would be "damaging to the relationship" between Mr Blunkett and the boy, he added.
The row has left Mr Blunkett fighting for his political life.
Friends of the Quinns have claimed Mr Blunkett fast-tracked a visa application for their former Filipina nanny, Leoncia Casalme. The Home Office has ordered an inquiry into the allegations.
A high-profile court battle is likely to further complicate Mr Blunkett's position. But there were reports he regards his children as a higher priority than his 34-year political career and may even be contemplating an exit from high office.
Mr Quinn, who was brought up in an orphanage in Thomastown, Co Kilkenny, pleaded for a ceasefire on Thursday after his wife was admitted to a London hospital suffering stress, said to have been brought on by the public row with Mr Blunkett.
Mr Blunkett, 57, and 44-year-old Mrs Quinn began their three-year affair just three months after she married Mr Quinn.
In the course of yesterday's judgment, it emerged that Mr Blunkett issued an application for a parental responsibility order and contact order on November 11.
The judge said there had been "inaccurate speculation" about the case and that Mr Blunkett had never sought a residence order or scientific paternity tests.
In his application, Mr Blunkett was described as the father of the child and Mrs Quinn as the mother.
Mrs Quinn did not accept that Mr Blunkett was the father and if she was right, his application for a parental responsibility order would be fatally flawed, said the judge.
He said he was giving his ruling in public at the invitation of Mr Blunkett's lawyers to set right some mis-reported facts and maintain the reputation of the family courts.
If it was contested that Mr Blunkett fathered Mrs Quinn's unborn child, separate proceedings would have to be begin after the birth, Mr Justice Ryder added.