Seamus Coleman's goal in the 56th minute was enough for the home side to claim a 1-0 win at the Aviva Stadium.
After Martin O'Neill's side were out-played for large parts of the game, they will be relieved to have come away with all three points.
Coleman, who captained Ireland for a first time in a competitive game at the Aviva celebrated his 40th international cap with his first Ireland goal.
Meanwhile, Robbie Brady has beeen taken to hospital for a precautionary scan, but the Norwich midfielder is concious and talking to medical staff after he suffered a nasty clash of heads during the second-half.
Brady is now a serious doubt for Sunday's trip to Moldova, while Jeff Hendrick will also miss that game after picking-up a yellow card during the closing stages tonight.