The actor was in Italy when Zach approached him out-of-the-blue and introduced himself.
Robert, 45, said on first appearance he thought that Zach looked very strange and didn’t recognise him, which made the actor a bit touchy.
"Before we started shooting I was down in Venice and some weird guy walks by and goes, 'Hi I think I'm doing a movie with you and Todd Phillips'," Robert is quoted as saying. "I thought 'I might have to punch this guy.' And then I realised 'Oh my God, that's Zach'. We have definitely come a long way since then."
The pair are now good friends after starring in Due Date together.
The film features a stressed-out father-to-be who has to hitch a ride in order to get to his child’s birth on time.
Zach has described how Robert and director Todd Phillips used to argue over how scenes should be played out in the film.
"Robert has his opinions. And I love to watch him give his opinions because he's incredibly eloquent and he makes me laugh,” Zach said of Robert.