Ireland claimed their first Triple Crown in 19 years but they failed to rack up enough points to give them a chance of winning the Six Nations.
The home side had a nervy first period against a fired-up Scotland team but Geordan Murphy's try just before the break gave Ireland a 16-9 lead.
Scotland did level the scores through an Ali Hogg touchdown on 48 minutes.
However three tries in the final 24 minutes, including a second for Gordon D'Arcy, sealed the win for Ireland.
There was a lot at stake for both sides heading into the game and the opening exchanges were nervy and fractious.
The visitors were first on the board, captain Chris Paterson slotting over after two minutes although fly-half Ronan O'Gara replied soon after for Ireland.
Scotland, stung by criticism of their displays so far in the championship, were robust in defence and their aggression seemed to knock Ireland out of their stride.
However the men in green scored the game's first try on 19 minutes when in-form centre D'Arcy finished off a fine move.
O'Gara extended the lead with a penalty six minutes later but the score did not dampen Scotland's enthusiasm as they started to dominate the game with some confident play.
They got the points their pressure deserved when fly-half Dan Parks, impressing in his first game for his country, fired over a drop goal from almost 40 metres out to reduce the deficit to two points.
O'Driscoll was earning his 50th cap for Ireland
But just as the Lansdowne Road crowd were preparing for a nervy half-time cup of tea, Murphy crossed in the corner after some silky back play to ease the pressure on the home team.
Scotland were unbowed and started the second half as aggressively as they did the first.
Even though they lost number eight Simon Taylor with a serious looking knee injury in the opening stages, Scotland levelled the scores through Hogg's close-range try and Paterson's conversion.
Kicked into gear by the try, Ireland piled forward and flanker David Wallace used his strength to power over on 56 minutes with O'Gara landing his first conversion of the game to make the score 23-16.
The visitors continued to battle bravely but the match was effectively sealed when Ireland scrum-half Peter Stringer burst from the bottom of a ruck to slide over.
The game lost its intensity as the clock started to tick down, but D'Arcy had the last word when he crossed for a his brace to kick-start the Dublin celebrations.
Ireland: G Dempsey, S Horgan, G D'Arcy, B O'Driscoll, G Murphy, R O'Gara, P Stringer, R Corrigan, S Byrne, J Hayes, M O'Kelly, P O'Connell, S Easterby, D Wallace, A Foley.
Replacements: F Sheahan, Horan, D O'Callaghan), V Costello, D Humphreys, G Easterby, K Maggs.
Scotland:: C Paterson, S Danielli, T Philip, A Henderson, S Webster, D Parks, C Cusiter, A Jacobsen, G Bulloch, B Douglas, S Murray, S Grimes, J White, S Taylor, A Hogg.
Replacements: R Russell, G Kerr, N Hines, J Petrie, M Blair, B Laney, D Lee.