A Kavanagh College pupil was walking across the Oval about 9.20am when she was confronted by a man who asked if she would walk with him to the Dunedin Public Library, Detective Sergeant John Hedges, of Dunedin, said.
When he attempted to touch her, she yelled and ran to a nearby store on Princes St to raise the alarm, Det Sgt Hedges said.
Wayne van Gorp, the 43-year-old co-owner of engraving firm Brandwell Moller, was serving a customer when he was alerted to the incident by office administrator Lesley Gillies.
Spotting a man who was running from the Oval in the direction of Andersons Bay Rd, Mr van Gorp - a Hill City Athletic harrier - took off in pursuit.
"I didn't know what he was capable of, so I kept my distance."
Keeping about 50 metres behind the man and remaining on the opposite side of the road, Mr van Gorp walked, jogged and ran, pacing the man for several kilometres along Vogel St, to Jetty St before he crossed Princes St.
Receiving a call on his cellphone asking him to pinpoint his location, he was able to tell police the man had entered a particular street address.
Police arrested a 37-year-old man soon afterwards.
Mr van Gorp's actions inspired praise from Det Sgt Hedges, who said his quick thinking and actions led to the arrest of the alleged offender.
The man, facing a charge of assault, was remanded on bail when brought before the Dunedin District Court later in the day.
Kavanagh College principal Paul Ferris confirmed the girl is a pupil at the school, and that she was playing truant at the time of the incident.
It was the second suspicious incident in a week involving a Kavanagh College pupil, he said.
Last week, a pupil of a similar age told a teacher she had been "followed or tracked" into the Dunedin Public Library by a man.
Mr Ferris said staff advised the pupil to report the incident to the police.
Det Sgt Hedges said police were now investigating at least four other similar incidents during recent weeks.
Det Sgt Hedges praised the responses of the young girl and of Mr van Gorp.
"We're very pleased with the girl's actions.
"And also the member of public who followed him and led us to him. He helped us get a quick result."
Mr Ferris said the girl was "OK", but the incident served as a warning to pupils who played truant from school.
"When you are out and no-one knows where you are, you leave yourself open to other people who want to take advantage of you.
"It's a danger - a real danger.
"We can't guarantee a pupil's safety when they are in a place they are not supposed to be."