The first goal of Marc Wilson's senior international career handed Ireland a 46th-minute lead in Torshavn and when Jon Walters made it 2-0 seven minutes later, three World Cup qualification points looked to have been banked.
Substitute Arnbjorn Hansen reduced the deficit with 22 minutes remaining but defender Pol Justinussen's 73rd-minute own goal and Darren O'Dea's late header ended hopes of a fightback.
The Irish ran out knowing the 90 minutes ahead might prove crucial in more than one way with their hopes of World Cup qualification facing significant damage if they did not emerge with three points, and Trapattoni's future hanging in the balance.
Trapattoni handed 20-year-old Manchester United winger Robbie Brady the task of improving the supply lines and he certainly added some vigour down the right and might have unlocked the Faroese defence on several occasions during the early exchanges, but - as the half wore on without the deadlock being broken - the home side grew in confidence and exerted genuine pressure.
The opening goal arrived just 43 seconds after the restart from an unexpected source. Wilson picked up possession wide on the left and cut inside before unleashing a 30-yard effort which flicked the head of full-back Jonas Naes and flew past the helpless Gunnar Nielsen and into the top corner.
In an instant, the tension lifted and Ireland increased their lead within seven minutes. On this occasion, Wilson turned provider, crossing from the left for Walters to head firmly towards goal, where Robbie Keane did enough to put off Nielsen, but not enough to justify his claims that he had got the final touch.
But just as it looked as though Ireland had the points wrapped up, they allowed Naes to make ground down the right and cross for Hansen to climb above John O'Shea and head firmly past Keiren Westwood.
However, hopes of a fightback were dashed within five minutes when, with the Faroes pushing for an equaliser, Walters broke into space down the left and sent in a cross which Aiden McGeady could not reach, but Justinussen turned into his own net.
O'Dea's 88th-minute header capped a comprehensive victory and perhaps - but only perhaps - gave Trapattoni a little breathing space.