Cops used a trail of blood drops to track down the suspect in Monday’s fatal stabbing of a Brooklyn mother at a subway station, police sources said Tuesday.

The female suspect accidentally cut her own hand during the Monday night attack, leaving behind drops of blood that ultimately led police to her grandmother’s home about 10 blocks away, sources said.

When officers, who also used surveillance video in their probe, arrived at the home, a relative told them the woman had been in a fight and had gone to a hospital, where she was soon found and arrested, sources said.

Authorities recovered the clothes the woman had apparently been wearing at the time.

Investigators on Tuesday were grilling the 20-year-old, who was picked up earlier in the day and brought to the 73rd Precinct, sources said.

The victim, identified as 30-year-old Latanya Watson, was aboard the northbound train when a dispute with the other woman started, police said.

The argument continued when the pair both got off the train at the Sutter Avenue-Rutland Road station in Brownsville at around 9:20 p.m.

Cops said that Watson pepper-sprayed the woman, who then stabbed Watson multiple times in the face, neck and arm in the mezzanine of the station.

Medics rushed Watson, who lived just blocks from the train station, to Brookdale Hospital, but she could not be saved.

It was not immediately clear what the argument between the victim and the suspect was over.

Watson had a 12-year-old and worked at Fairway Market in Red Hook, family members and neighbors said Tuesday.

“I’m angry!” said Watson’s father, Frank, who said his daughter was on her way home from work when she was fatally knifed.

“She was my daughter,” the devastated dad said. “This is an unfortunate situation.”

The victim’s aunt, Joan McGriff, said the family is “in shock.”

“She was a beautiful young woman. She was educated. She never looked for trouble,” McGriff said. “She is a mother…She smiled a lot. She’s very smart, respectful, she minds her manners.”

Watson’s fiancé, Jerelle Martin, told CBS New York that her death “still does not feel real.”

“She was my queen. She was the most beautiful woman I ever met in this world,” Martin said.

A neighbor of Watson’s said she had her son just before she moved to Brownsville where the victim lived for 12 years.

“She loved her boy,” the neighbor said.

Additional reporting by Stephanie Pagones and Natalie Musumeci