The second seed had looked a little rusty in his opening win over Fabio Fognini, losing the first set, but today he was on form from the first shot.
The result meant a huge amount to Baghdatis, who will now meet third seed Andy Murray in a repeat of their late-night clash at the same stage of Wimbledon a month ago.
The 27-year-old said: 'It's great emotions. I want to thank whoever is up there for giving me this chance to be part of this life, and that's why I kissed the court.
'I am in the last 16 of an Olympic event and that's an incredible thing for me, and I hope I will keep going.'