Five people, including a four-year-old boy, were inside the house in Harefield Road, Speke, Liverpool, at about 19:35 GMT, the time of the shooting.
A 22-year-old man was injured in his torso by a "shotgun discharge" fired through the window, police said.
A woman, aged 21, and another man, 29, were hurt by the glass. Police said the property was "mistakenly targeted".
The woman, who suffered facial injuries, and the 29-year-old, who was grazed on the arm, have been discharged from hospital.
The 22-year-old was left with pellet wounds in his torso and remains in hospital.
Police believe the shooters left the scene in a stolen black Volvo that was found burnt out less than a mile away in Rycot Road at about 04:50.
Officers have spoken to witnesses and CCTV footage is being sought.
Supt Matt Boyle said: "Three people received injuries as a result of this attack, but it could so easily have been more and among those inside the house, but thankfully unhurt, was a four-year-old boy.
"I am sure the community will share our shock and distress at the fact that people could be shot as they sit in a living room."
Two men and a woman have been injured after a shotgun was fired at a living room on Boxing Day.