The couple, who were approaching to land at Blackbushe Airport, told witnesses "it was a matter of life and death" after they walked away from the plane unscathed.
The aeroplane was coming from France when it was forced to make an emergency landing at Hill Farm.
Farmers who witnessed the landing said the Piper Warrior four-seater light aircraft suddenly appeared and came down with an almighty bang at about 3.30pm — just yards away from trees by Heathlands Cemetery, Steven's Hill, Yateley.
But miraculously both the male pilot and his female passenger walked away uninjured but shaken.
The Air Accidents Investigation Branch is now investigating the incident to see what caused the plane to make the emergency landing.
"I looked around and saw something like a plane coming through trees but I didn't hear anything," recalled John Baggs, a relative of the landowner at Hill Farm, who was working in the field at the time. "I heard an almighty thud — he came straight in and just stopped."
Mr Baggs believes hay in the field cut for baling may have broken the plane's landing, saying: "If it hadn't been for the hay wrapping round the wheels he'd never have stopped. The hay bunched up in the field — otherwise he could have ended up in the trees in the cemetery."
Mr Baggs said he and his cousin Tony alerted the emergency services and rushed over to see if the pair were alright. "They were a man and a woman from Southsea. They were both clearly very shaken by it," said Tony Baggs.
He said five fire engines, two paramedics and an ambulance were on the scene within minutes.
A Hampshire Fire and Rescue spokesman said the plane may have run out of fuel, but it landed safely and nobody was hurt.
It will be up to the AAIB to decide why it came down.
A Blackbushe Airport spokesman said the plane had engine problems and made a safe landing in a field approaching the airport.
"The scene was attended by local authority emergency services and the Airport Fire and Rescue Service. The circumstances of the incident are being investigated."
A spokeswoman for the AAIB said she was unable to make any comment until the results of its inquiries were known.
Pictured from left are Tony Baggs, John Baggs and Phil Coombes, who were first on the scene of the emergency landing. The stricken aircraft is in the background.