Police say the two incidents - believed to be linked - happened over the course of several hours.
The first, reported shortly after 11pm, saw a 24-year-old man stabbed near to Estcourt Avenue, with his mobile phone and a wallet stolen.
The second, reported at 3am, saw a 22-year-old man injured near to The Arc, at the corner of Ash Road, as he was taking cash out of an ATM machine.
Both men suffered serious injuries, police have said, and were taken to Leeds General Infirmary for urgent medical treatment.
A 19-year-old man, arrested in the area shortly afterwards, is being questioned by police and remained in custody this morning.
"Both the victims were stabbed and received injuries that were treated in hospital," a spokesman said.
"A short time later a male was arrested in the area. He is still in custody and police are searching the area.
"Some areas have been taped off while we search the scenes."
Police had cordoned off parts of North Lane between Otley Road and Headingley Stadium this morning.
Anyone with information is asked to contact Leeds CID via 101 quoting reference number 13180152345.