A nightmarish string of medical errors left a Long Island baby dead, and her grieving parents were falsely accused of abuse, according to a lawsuit.

Sara Keenan, 35, had breastfed baby Lana and put her down for a nap on Jan. 3, 2014. About an hour later, the dad, Padraig Keenan, 37, found the 3-month-old in her crib, choking on her own vomit, they claim.

Miraculously, a houseguest who works as an EMT quickly revived the baby, who began to breathe again.

The parents then called 911, unknowingly igniting a chain reaction of medical missteps that doomed their tiny daughter, according to their suit.

Emergency medical technicians from Exchange Ambulances of the Islips failed to intubate the infant, give oxygen, or even protect her from frigid temperatures as they carried her to an ambulance parked four doors away, according to court papers filed last week.

Instead of taking the child to pediatric intensive care units at nearby Good Samaritan or Stony Brook hospitals, the medics brought her to Bay Shore’s Southside Hospital. There, an emergency-room doctor pumped the 12-pound girl with a “cornucopia of drugs,” including Propofol, the powerful sedative linked to Michael Jackson’s death.

The deadly cocktail lowered the infant’s blood pressure so much, oxygen didn’t get to her brain for at least an hour. An attempt to correct the condition with epinephrine, meant to raise Lana’s blood pressure, failed when an IV was incorrectly inserted, the suit claims.

The baby was then brought more than an hour away, to Cohen Children’s Medical Center in Queens. Cohen and Southside are part of Northwell Health, formerly known as North Shore-LIJ.

At Cohen, Dr. Jamie Hoffman-Rosenfeld entered the picture, introducing herself to the Keenans as “Dr. House,” the quirky but brilliant TV diagnostician.

She decided the infant had shaken-baby syndrome, the suit claims.

Hoffman-Rosenfeld led “a bogus, illegitimate, and wholly contrived witch hunt falsely accusing both of harming their child and causing the injury which ultimately led to her death,” the Brooklyn federal court suit says.

“The type of brain damage [Lana] sustained did not even closely resemble what is seen in ‘shaken baby syndrome’ or cases involving intentional or accidental ‘traumatic head injury,’ ” according to the lawsuit.

As Lana lay dying, the doctor and Suffolk County social workers secured orders of protection barring the parents from being near their infant, and took custody of their sons, 6 and 3.

Suffolk County cops and the Suffolk District Attorney’s Office investigated Hoffman-Rosenfeld’s findings but uncovered no criminality. Two autopsies later confirmed that no physical abuse occurred.

But the child protection agency pursued a custody case, alleging parental abuse, in Suffolk Family Court for 11 months after Lana’s death in February 2014.

The Keenans were finally cleared in January 2015.

The contractor and his wife, who has since given birth to another daughter, believe the Family Court case was pursued to pressure them into making a false confession and clearing the medical community of culpability.

The couple want unspecified damages from Hoffman-Rosenfeld, Northwell Health, Suffolk County, the ambulance company and others.

Northwell Health noted that state law requires health workers to report child injuries.

“The loss of a child obviously is a tragedy, and we have extended our sympathies to the family,” spokesman Terry Lynam added.