The Hollywood star and his minder were several hundred metres ahead of the pair, but they managed to catch up with them near the Octagon.
''You only get one chance, and I don't know anyone who isn't a fan of him, to be honest ... he is James Bond,'' Caley said.
Alfred then asked the actor: ''Excuse me Daniel, could I have a photo with you?''
The actor was friendly and asked the pair of Otago Boys' High School pupils where they went to school.
''I told him it was good to meet him, as it was not often you get to meet a celebrity in Dunedin,'' Alfred, who had watched all of Craig's movies, said.
Caley told the Otago Daily Times: ''To be quite honest, I don't think he wanted to be seen, because he had the cap and glasses on, but he seemed to be enjoying himself down here.''
The pair had been aware he was in town with his wife, Rachel Weisz, who is in Dunedin filming The Light Between Oceans, which also stars Michael Fassbender.
Meanwhile, the cheeky pair were enjoying their moment in the spotlight.
''We chased James Bond down ... they could make a movie out of that,'' Caley said.