Ireland manager Vera Pauw labelled this as a 'must-win' game to boost their chances of qualifying for next summer's UEFA Women's European Championships and they completed that task.
In front of 4,511 spectators, the home side dazzled in patches with Player of the Match Ruesha Littlejohn pulling the strings like a master puppeteer and Denise O'Sullivan bemusing her opponents with sublime pieces of skill.
The chances came early on with Littlejohn whistling a shot over the crossbar from the distance before O'Sullivan forced the visiting goalkeeper into a save on 10 minutes.
Louise Quinn went close with a header but she made up for it just before the interval when connecting with Katie McCabe's free-kick and sending the ball into the path of the unmarked Caldwell to slot in.
It was Caldwell's second senior goal and it proved to be a vital one as Littlejohn again had the home crowd gasping when an excellent effort sailed just wide of the goal.
Ireland will now travel to Montenegro ahead of their clash on March 11, but this victory - and maintaining their unbeaten run in Group I - keeps them in a good position for qualification.
Republic of Ireland: Hourihan; Scott, Caldwell, Quinn, O’Gorman; O’Sullivan, Fahey; Payne (Russell 63), Littlejohn (Shine 86), McCabe; Jarrett (Barrett 71).
Greece: Papakonstantinou; Chatzigiannidou, Sidira, Chatzinikolaou; Gkatsou, Kakambouki, Markou, Kynossidou (Spyridonidou 83); Moraitou (Vardali 65), Kokoviadou, Kongouli (Sarri 66).
Referee: Maria Dolores Martinez Madrona (Spain).