The driver managed to escape from the situation with only minor injuries after the sinkhole formed following a water leak on Wednesday morning.
The dogs, Spike and Spay, became trapped in the sinkhole after falling in while playing on the edge.
The hole, first spotted by walkers at a popular tourist spot, is the size of half a tennis court and is expected to grow.
Photos and videos taken from the scene in Puebla, Mexico, show huge chunks of earth falling from the rim and into the hole beneath.
The sinkhole initially measured around 15ft in diameter, but grew to 200ft across and 50ft deep in a matter of hours.
Leonard Shoulders, 33, was waiting for a bus in the Bronx when the sidewalk collapsed beneath his feet.
A woman who had visited a "heave mound" before an explosion almost became the "first victim" of the geological event, a scientist studying the crater said.
The man told authorities that he drove around the barricades because he didn't realize they were to cordon off a large hole.
Footage published by the Citizen app shows a vehicle sunken below ground level in East Village, Manhattan.
The 30-year-old was suffering from a tooth abscess, arthritis and a bacterial brain disease when she was killed 9,900 years ago.
"Please avoid sight seeing at this location. It's not safe as the sinkhole is still active. One of the homes fell in this evening. Several families are hurting as they are losing their home," police said.
The hole was caused by a water main break.
The storm event has resulted in mudslides, rockfalls and fallen trees across state routes.
This is the third sinkhole to open up where president Trump has been staying.
Richard Branson and Fabien Cousteau dove to the bottom of the Blue Hole in December.
Construction failures are thought to have caused the pit, which measures about 100 ft wide and 50 ft deep.
The woman, whose identity remains unknown, was rescued by local police in Lanzhou City and suffered fractured ribs.
The "world-class" cave complex has a volume of 236 million cubic feet.
The ground opened up without warning in a busy district of Dazhou city, Sichuan province.
The two families were able to evacuate safely and declined help from the American Red Cross, officials said.
"She did ask for a headlamp on Mother's Day," the comedian quipped.
Over the past week, at least a dozen sinkholes have opened up in a single neighborhood in Ocala.