Rockland County prosecutor Dominic Cristino called the killing of grade-school teacher Jami Erlich "vicious and heinous."
Town Judge Scott Ugelo ordered Lau held without bail.
He's accused of killing the 32-year-old Erlich on Sunday night. The gym teacher was found dead in her Valley Cottage condo.
Clarkstown police said they received a call from a citizen about a suspicious person walking along Phillips Hill Road in New City.
As a patrol car approached the individual, he ran into the woods and hid from police. Police surrounded the area and used dogs to track him down.
They eventually found Lau lying on the ground and took him into custody at 7:30 p.m.
Lau grew up near where his car was found in New City on Tuesday morning, sparking a search that included the Rockland County Sheriff's helicopter and police with bloodhounds on the ground.
The body of Erlich, a physical education teacher at Connor Elementary School in Suffern, was found inside her own home on Monday.
"It's horrible. Just horrible. Life is over like that," Linda Brown said.
Brown and others in the Valley Cottage complex in Rockland were unnerved after learning Erlich was murdered in her ground-floor condo.
Neighbors say Erlich had only moved into the condo a few months ago.
The medical examiner ruled that Erlich died from a combination of bludgeoning and stabbing.