Jordan Mutch made a bright start to life with his new club, taking a shot just five minutes into the tie, but pulling the ball just wide from a tight angle.
Mutch continued to look a threat for the hosts, linking up with Charlie Austin up front, but the pairing continued to be frustrated by the PAOK defence.
Shaun Wright-Phillips also tried to create a chance for Austin, but the striker was well marked, allowing the Greek side to clear the danger.
However, PAOK were able to edge ahead with just over an hour played when Hill turned a Facundo Pereyra cross into his own net.
Mutch tried to set up an equaliser with just over 10 minutes to spare as he picked out Bobby Zamora with a cross, but the striker headed well over.
Pereyra came close to doubling PAOK's advantage late on with a powerful shot, but it was held by Green, ensuring that the Hoops lost by just the one goal.