It happened just before 4 a.m. in the 2600 block of Westerland Drive.
Witnesses said they heard screaming as a couple was arguing outside before shots rang out, according to Houston police.
Residents found the bodies of a man and a woman in a black Ford Mustang outside. Both had gunshot wounds, police said.
It appeared the man shot the woman to death before turning the gun on himself, police said.
The female victim was identified as 24-year-old Itzell Sanchez. The 21-year-old man was not immediately identified. Both were pronounced dead at the scene.
Police believe the two were in a relationship for around the past year, and it wasn't immediately clear what led to the tragedy.