The couple had thought they were safe inside the white Toyota while touring through the Lion Safari Park in Johannesburg, South Africa, the Daily Mail reports.
But the 135kg lion surprised the pair by gripping a backseat door handle between its teeth and yanking the door open.
According to one witness, the white Toyota sat motionless for several seconds as the lion and the pair eyed each other off.
The driver hit the accelerator moments later but the lion gave chase, keenly pursuing the car all the way to the gates.
A park employee finally managed to distract the animal by throwing a large stone.
British tourist Richard Holden said he was stunned as he watched the saga unfold from a vehicle nearby.
"They must have been panicking because they didn't drive off straight away," Mr Holden told the newspaper.
"If that had been me, I would have hit the gas."
He said visitors had been warned to lock their doors and windows before entering the reserve.
Park staff said the lion presented little danger as all animals there were well fed.