Cops this week busted a third suspect allegedly involved in the box cutter slashing of a retired NYPD lieutenant — and the sexual assault of his wife — inside their Brooklyn home last month.

Tyrique Rushing, 20, who is homeless, was apprehended in Missouri and extradited back to New York Friday where he faces a slew of charges — including attempted murder, robbery, assault, burglary, grand larceny, criminal sex act, sex abuse, unlawful imprisonment, and unauthorized use of a vehicle, authorities said.

Rushing, and two other goons, slipped into the couple’s Marine Park home through an unlocked door early on Oct. 8 and went upstairs, where they found the 72-year-old retired officer and his 71-year-old wife sleeping in separate bedrooms, sources said

The thieves woke up the couple and told them “if you say anything you’re dead,” before demanding cash and jewelry, according to sources.

When the retired cop refused, one of the thugs slashed him in the face with a box cutter, sources said.

Then one of the fiends sexually assaulted the elderly woman, who had been bound by duct tape, according to sources.

The retired cop, who did not appear to be bound, grabbed a .38 caliber handgun, which sent the criminals packing.

They fled in his 2012 Honda Civic, which was spotted later driving over the Brooklyn Bridge and the George Washington Bridge toward New Jersey, sources said.

Hours later, Lance Jyriken, 20, and Shirnel Sobers, 25 — also homeless — were busted inside the same car.

The couple was taken to Maimonides Medical Center for treatment, police said.

Rushing is expected to appear at Brooklyn Supreme Court next week, a court clerk said Saturday.

Additional reporting by Olivia Bensimon