The body of India Chipchase, 20, was found under sheeting on a mattress at a house in Stanley Road in Northampton on 31 January.
Edward Tenniswood, 52, of Stanley Road, Northampton, denies murder and rape.
Christopher Christon saw Ms Chipchase "stumbling" across the road near NB's club in Northampton.
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He told Birmingham Crown Court he was waiting for a lift home with his wife Jacqueline near the club at about 01:00 GMT on Saturday 30 January when he saw Ms Chipchase on her phone.
He said: "She seemed quite distressed. I think she was trying to get through to someone. It seemed like she was crying."
Ms Chipchase was outside the club after she got separated from her friends inside, when at about 01.15 she was approached by a man who the prosecution have claimed was Mr Tenniswood.
Mr Christon said he saw an older man wearing a Parka-type jacket and a rucksack get "all the way up" to Ms Chipchase and "put his arm around her".
The witness said he was concerned enough to tell his wife to keep watching, but it did not appear to him that Ms Chipchase responded to the older man in any way during a 20-minute period.
Samuel Stein QC, defending, asked: "Did it look like the girl was ignoring the bloke?"
Mr Christon replied: "I just think she was that drunk that she didn't know what was going on."
Jurors have heard about DNA and fingerprint evidence from examinations of Mr Tenniswood's rented terrace house in Stanley Road, Northampton, where Ms Chipchase's body was found.
Laboratory tests on a cigarette butt discovered in a cup in the kitchen bin found DNA matching only that of Ms Chipchase.
The trial continues.
A student who was found raped and murdered after a night out appeared so "drunk she didn't know what was going on", a court has been told.