Christos Tzolis made a late addition to the scoreline with a brilliant run and finish, securing a crucial goal for Group B2 leaders Greece who now have six points from their first two matches. Unfortunately for Ireland, this marked their second loss in the tournament.
The visitors led after 50 minutes when Ioannidis was given far too much time and space to pick his spot from 25 metres and brilliantly curled the ball into the back of the net.
He scored twice in the 3-0 home win over Finland on Saturday, which should have been a warning for Ireland but one that was not heeded.
The points were safe when Tzolis used his pace to get behind the Ireland defence three minutes from time and showed composure in the box before drilling the ball low into the net.
Ireland winger Chiedozie Ogbene had netted a superb strike from 25 metres four minutes before halftime but was offside in the build-up.
Ireland travel to Finland and Greece for their next two games in October, while the latter also play England, who are in second place also with six points, at Wembley.