Elaine Davison, 55, suffered fatal injuries after the 13ft branch crashed through the windscreen of the car she was travelling in with her husband in Wakefield, West Yorkshire, in November 2010.
Edward Davison struggled to contain his emotions as he told an inquest about the events leading up to his wife's death.
Mr Davison, who had been in a relationship with Mrs Davison for 30 years, told the jury of seven women and four men that his wife told him she was hurt after the tree hit their Vauxhall Zafira.
He said: "The only other thing she said to me was 'don't let me die, will you?' and I said 'no, I won't'.
"That's one of the hardest things. It's the first time I've ever had to lie to her and I can't take it back."
Coroner David Hinchliff read Mr Davison's statement to him and described how the couple had been to visit their daughter at Pinderfields Hospital before setting off to return home to Pontefract.
Mr Hinchliff said: "You said it was very windy and recalled Elaine pulling her coat collar up to keep the wind out."
Mr Davison said he could see small tree branches on the road and feel them beneath his car as he drove along the A642 Aberford Road.
The coroner said: "The wind was actually blowing your car along, you could actually see the car shaking from side to side while you were driving.
"You remember Elaine saying to you she 'didn't like this' and appeared nervous. She asked if you were speeding, which you told her you were not. You could see she was frightened at the time.
"You reassured her 'Don't worry, we'll be tucked up in our pyjamas in 20 minutes'."
Mr Davison described a sudden "banging and crashing sound" as the tree branch fell into the road directly in front of the car, before hearing "silence" after the impact.
The inquest heard how the windscreen was pressed in over Mr Davison and his wife and he could see something "wood-like" pressing against Mrs Davison's stomach through a hole in the glass.
Mr Hinchliff said to him: "You describe going into what you say was a blind panic.
"You asked Elaine if she was OK, but she said 'no, I'm hurt'."
He continued: "Elaine was saying she couldn't breathe, she was holding the tree branch up against her stomach, she was saying 'get it off'."
Mr Davison described "frantically" breaking small branches from the tree so he could get to his wife and flagging down a passing ambulance to help.
The inquest heard that Mrs Davison was taken to hospital, where she was pronounced dead after attempts at resuscitation.
A post-mortem examination found that she had died from injuries consistent with the branch of a tree penetrating through her abdominal wall.
Michael Ferries, watch commander with West Yorkshire Fire and Rescue Service, attended the scene on the evening of November 11 2010 and said the weather conditions were the worst he had experienced.
He told the inquest Mrs Davison had been "impaled" by the branch, which he described as being 12-13ft long and 7ins in diameter at its widest point.
He said he became concerned about the condition of remaining trees because of the "cracking" noise they were making.
The inquest heard that Mr Davison had given a negative breath test on the evening and collision investigations found no evidence he had been speeding, the vehicle was in good condition and there were no problems with the road surface.
Mr Hinchliff said Mr Davison would have had no prior warning of the branch falling and would not have been able to avoid the impact.
The inquest at Wakefield Coroner's Court, which is due to last around 10 days, was adjourned until Tuesday.