Ireland started confidently and dominated with the ball in the early stages, before Ian Madigan capitalised on a penalty to score the first points of the afternoon.
However, they were soon level again when Valentin Calafeteanu split the posts from close to the touchline after Romania's first drive forward.
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The Irish supporters were in full voice when Simon Zebo appeared to put them ahead with a stunning piece of play on the wing, but replays cut the celebrations short when it was confirmed that the full-back had a foot out of play while retrieving his low kick on the way to sliding over in the corner.
A second penalty from Madigan did restore their advantage, and Joe Schmidt's side then delivered the first try of the match with a move that started with Earls claiming a high catch before the ball moved across the pitch quickly to reach Bowe, who survived the latest decision from the TMO by holding off a challenge to cross on the slide.
Another piece of impressive play from Zebo handed Ireland full control before the interval as he took three Romanians out of the game with an excellent pass to Earls, and the Munster wing was at full stretch to score the try in the corner before Madigan struck the post with his conversion attempt.