Firefighters responded to the blaze at approximately 7:45 p.m. after receiving an automatic alarm from an eigth-floor unit at the Cambridge Tower.
Crews arrived to find smoke coming from a unit on that floor and evacuated 100 of the 170 residents, the report said.
An 88-year-old man and a 79-year-old woman were rescued from balconies on the same floor and were transported to St. David's Hospital with orthopedic injuries.
A resident was rescued from the apartment where a candle ignited the Christmas tree, but it wasn't clear if he was taken to the hospital.
Four other residents also were evaluated.
The fire was extinguished by 8:30 p.m.
The cause of the fire was deemed accidental and damages are estimated at $250,000 to the building’s structure and $100,000 to contents.