Munster fly-half Ronan O'Gara booted all of Ireland's points and Eddie O'Sullivan's men travel to Twickenham next weekend where they will hope to clinch their first tournament title since 1985.
All of Scotland's points came from the boot of Chris Paterson with defeat ending their own RBS 6 Nations title challenge.
Ireland entered the interval 12-9 ahead following a finely-balanced first half marked by some ferocious Scottish defence.
There was no shortage of possession to fuel the home side's attacking ambition but they were consistently met by a wall of blue shirts.
The Scots' haste to advance meant they often strayed offside, however, and O'Gara punished the infringements with four penalties.
Scotland replied with three from Chris Paterson and with the wind behind them, Ireland were expected to take a stranglehold on the game in the second half.
But Frank Hadden's side, under heavy pressure for long spells, frustrated their opponents with their aggressive defence keeping them in touch.
O'Gara added another penalty to stretch their lead to 15-9 and despite piling on the pressure they were unable to add to their score again.