Police constable Dave Fields, who was 46, was responding to a call when the police car he was driving and another vehicle travelling in the opposite direction collided on the A57 near Shirebrook Valley Nature Reserve at around 8.15pm.
He was pronounced dead shortly afterwards and Sheffield woman Lorraine Stephenson, 61, who was a passenger in a Citroen C3, died in hospital.
A 63-year-old man who was driving the Citroen was also taken to hospital, where he remained yesterday in a serious condition.
It comes as other fatal road collisions have taken place across Yorkshire during the Christmas period.
A 20-year-old man has died after a road collision in Bradford yesterday morning.
Officers were called shortly after midnight to Whetley Lane, near to the junction with Fairbank Road, in Manningham.
The man was taken to Bradford Royal Infirmary after a grey Peugeot 107 and a grey Vauxhall Astra collided, but was pronounced dead at the hospital.
West Yorkshire Police also yesterday confirmed that a 26-year-old man died after a road collision on Wakefield Road in Ackworth, near Pontefract, on Saturday.
A blue Peugeot 206 and grey Ford Kuga collided at around 11.23am, with a 59-year-old woman also suffering minor injuries.
An online fundraising page has been set up to raise £1,000 for the families of the officer and the woman in the Sheffield collision.
Trevor Sherwood, editor of Crime and Policing News Website, who set up the page, said: “Please help and support the family of these victims. This is a very tragic incident that has happened on Christmas Day.
“We have lost a member of the thin blue line and tragically a member of the public also. A police officer should never have to leave his family on Christmas day knowing he’ll never return.
“My thoughts are with both families and those officers, paramedics and fire crews who attended his tragic incident. Let’s raise as much as we can in the memory of these fallen victims.”
Assistant Chief Constable of South Yorkshire Police, David Hartley, said: “On behalf of the force I’d like to offer my sincere condolences to all of those left bereaved by this terrible tragedy, our thoughts, love and support are extended to all those affected.
“We are doing everything we can to support them through this difficult time.”
“We have lost a friend and a colleague from our police family in this incident,” Assistant Chief Con Hartley added.
“The officer has been with us for 12 years and was a passionate, professional and universally liked officer.
“His colleagues, and everyone across the force, are devastated by what has happened.”
The force has since issued a statement which reads: “We are aware of a fundraising page set up to collect donations for the families of those affected by this incident.
“Officers want to remind the public to be careful to verify any websites of this nature and only donate to legitimate pages.”
The Independent Police Complaints Commission is investigating the circumstances as a mandatory measure after being notified of the tragedy.