A court heard a child and two adults suffered burns during the incident at the blaze which was started by Darren Clifford.
Clifford cut the fuel pipe on the quad bike before setting it alight outside the house in Colwyn Terrace, Beeston, after a row with his partner.
Earlier in the evening, on August 30 last year, police had been called to the area to deal with a disturbance in the street and arrested Clifford.
Officers then took Clifford, 27, to stay with members of his family but he returned to Colwyn Terrace several hours later.
Leeds Crown Court heard ten of Clifford’s partner’s family members were in the property when he returned to the house but was not allowed inside.
Clifford then set the quad bike alight outside the front door. A fire engine was called to the property and two adults and a child suffered minor burns as they escaped. Around £6,000 of damage was caused.
Clifford, of First Avenue, Armley, pleaded guilty to arson being reckless as to whether life was endangered.
Mohammed Hussain, mitigating, said Clifford had originally bought the bike and decided to destroy it so no one else could use it after he was refused entry to the house.
He said Clifford had not intended to put anyone in danger but the bike had rolled towards the front door after he started the fire and he was unable to stop the machine. Clifford was jailed for two years, eight months.
Mr Hussain said: “He behaved in a foolish and reckless manner.”
Judge James Spencer, QC, told Clifford he had committed a “particularly serious” offence. He said: “Because of your disagreement you went to this house where she was living after midnight. You went round there to cause trouble.
“It seems to me that there must be a significant sentence of imprisonment.”