A police spokeswoman said they were called to Ormond Rd in Twyford, on the outskirts of Hastings, at 7.20am.
The crash was believed to have occurred earlier, at about 3.40am.
The Holden vehicle appeared to have failed to take a bend and collided with a tree.
Two men were transported to Hawke's Bay Hospital by ambulance with critical injuries.
A hospital spokesperson said they are still in a critical condition in the Intensive Care Unit.
Ormond Rd was closed near the intersection with Evenden Rd and reopened at about 11.40am.
Thee serious crash unit also attended.
Shockwaves rippled through the country last week following a two-car crash near Waverley which killed seven people - including a baby girl and her 8-year-old sister.
At least three other crashes also occurred on Hawke's Bay roads overnight and early this morning.
Emergency services were called to two crashes on State Highway 5 near Tarawera and Te Pohue and another on State Highway 2 near Takapau.
A Fire and Emergency New Zealand spokesperson said the incidents did not appear to be serious and no one was injured.
A police spokesperson said one lane of State Highway 5 was closed for a short time following a single-vehicle crash at about 10.40pm near Turangakumu Rd.
The vehicle had rolled and landed on its side but there were no injuries.
One person was processed for excess breath alcohol and inquiries are ongoing, she said.
Two people were also uninjured after the vehicle they were in rolled down a bank on State Highway 5, south of Te Pohue, at about 6.30am.
The occupants were out of the car and on the roadside when emergency services arrived.
Police are looking for a person who fled the scene of another single-vehicle crash after a car hit a power pole on State Highway 2 near Takapau at 12.53am.
