Giovanni Trapattoni's Ireland side bounced back from Friday night's 6-1 home defeat to Germany in convincing style with Marc Wilson scoring his first international goal just after half-time before Jonathan Walters made it two.
Arnbjorn Hansen pulled one back for the home side only for an own-goal from Pol Johannus Justinussen to restore the two-goal gap and Darren O’Dea also scored his first goal for Ireland late on to put a little gloss on the scoreline.
Ireland had an early chance in the 13th minute, but Keith Andrews headed wide from four yards following Aiden McGeady's cross from the right after a Robert Brady short corner.
At the other end, Daniel Udsen forced Ireland goalkeeper Keiren Westwood into a tip-over with a cross from the right before Faroes goalkeeper Gunnar Nielsen also impressed with a crucial save in the 26th minute.
Andrews found space in the home defence’s six-yard box to send a backwards header towards goal from Robbie Keane's superb chip into the area. Walters was closing in and got a touch on the ball as Nielsen dived to save, but the former Manchester City goalkeeper was able to push the ball away with a strong hand.
The Faroes had a clear sight of goal seven minutes before the break when Christian Holst set up Joan Simun Edmundsson on the left-hand side of the six-yard box and O'Dea had to hurl himself in front of the ball at the near post.
Ireland opened the scoring a minute into the second half. Stoke City defender Wilson cut inside past Udsen and unleashed a shot from 35 yards that took a deflection off Jonas Tor Naes and whistled into the top corner.
It was 2-0 seven minutes later when Wilson cut in from the left and crossed for Walters, who leapt above Justinussen to head towards goal. Keane got in front of Nielsen and the ball rolled in the net, but there was no touch from the Ireland captain despite his extravagant celebrations.
Inexplicably, Ireland tried to sit back on the two-goal lead, and substitute Hansen pulled one back for the home side when he climbed above O'Shea to head Naes's looped cross from the right past Westwood.
It came as a relief when Ireland restored their two-goal lead on 73 minutes, as Justinussen put through his own goal from Walters's cross from the left under minimal pressure from McGeady.
Ireland completed the scoring two minutes from the end when O'Dea headed in McGeady's corner at the back post, with Rogri Baldvinsson seemingly more keen to stop the Ireland defender’s run than challenging for the ball.
GERMANY 4-4 SWEDEN
Germany lost their 100 per cent record in stunning fashion after Sweden roared back from four goals down to draw 4-4 in a thriller in Berlin.
Miroslav Klose struck twice in the opening 15 minutes before defender Per Mertesacker made it 3-0 in a game watched by German Chancellor Angela Merkel and Sweden's Prime Minister Fredrik Reinfeldt.
Klose's goals were his 66th and 67th in international football, taking him within one strike of the country's all-time leading scorer Gerd Mueller.
Midfielder Mesut Ozil added a fourth goal 11 minutes after the break, chesting down a Thomas Mueller cross before firing a wicked shot past goalkeeper Andreas Isaksson.
Sweden captain Zlatan Ibrahimovic launched the fightback with a brilliant header from a long pass by Kim Kallstrom in the 62nd minute.
Mikael Lustig pulled another goal back before Johan Elmander cut Germany's lead to 4-3 in the 76th minute, striking a shot between defender Holger Badstuber's legs.
Rasmus Elm then grabbed the equaliser just before the final whistle.
Group leaders Germany have 10 points from four games while Sweden are second with seven points from three.
AUSTRIA 4-0 KAZAKHSTAN
David Alaba set up two goals for Marc Janko and scored one himself to help Austria to a convincing 4-0 win over Kazakhstan in a World Cup Group C qualifier in Vienna.
Martin Harnik completed the scoring to give Austria their first win of the campaign and leave them with four points from three games.
Austria were held 0-0 away by the same opponents on Friday but quickly took control and went ahead when Janko headed home 20-year-old Alaba's cross after 24 minutes.
The second goal was a near replica as Alaba, who plays left back for Bayern Munich and in midfield for his country, again crossed for Janko to head in after 63rd minutes.
Alaba, recently recovered from a stress fracture, crowned his performance by turning in Marko Arnautivoc's pass eight minutes later and Harnik completed an impressive win in stoppage time.