The game in Torshavn was goalless at the interval, but an Ian Harte penalty and a deflected Kevin Kilbane effort ensured Brian Kerr's side avoided an embarrassing result and returned to the top of Group Four.
Kerr made three changes to the side that drew 2-2 with Israel at the weekend, as Roy Keane and Stephen Carr returned from suspension and Stephen Elliott replaced the injured Robbie Keane.
The visitors started well and Clinton Morrison had the ball in the back of the net after just eight minutes, only for the offside flag to be raised.
The Irish did not have it all their own way and midway through the first half the Faroes were within inches of opening the scoring after a swift breakaway.
The ball eventually fell to Hedin a Lakjuni on the left side and his first-time drive beat Shay Given, but rebounded to safety via the post.
Harte tested home goalkeeper Jakup Mikkelsen with a 30-yard free-kick before Kerr's men had to survive another uncomfortable moment ten minutes before the interval.
Carr's mis-hit clearance struck Keane and fell to Andrew av Flotum, who smashed it through a crowded penalty area forcing Given into a smart stop.
In the 40th minute Elliott, on his first competitive start, should have given Ireland the lead after Mikkelsen made a spectacular save to deny Andy Reid, but the Sunderland forward hit the rebound against the crossbar.
The minnows continued to threaten after the break and Rogvi Jacobsen headed over before Elliott earned the crucial penalty in the 51st minute. The youngster was brought down by goalkeeper Mikkelsen and Harte smashed home the spot-kick.
Eight minutes later Kilbane made the game safe when a poor defensive header dropped to him 25 yards out and he drove the ball into the corner with the help of a vicious deflection off Faroes captain Oli Johannesen.
Elliott almost added a third a minute later when he beat Johannesen and Danielsen, only for Mikkelsen to save bravely at his feet.
The home side pressed hard in search of a consolation and Given had to be alert to keep out Lakjuni's long-range shot 15 minutes from time.
Given then endured a heart-stopping moment when he mis-hit a clearance against Flotum and was relieved to see the ball cannon to safety.
The Newcastle shot-stopper was called into action again in a nervy end to the game, charging out of his area to beat Claus Jorgensen to a long throughball and ensuring the game finished 2-0.