The Scots won by 46 runs in a game reduced to 45 overs, which puts them into the finals in England in 1999. They will face tough opposition as they are drawn in the same group as Australia, West Indies, Pakistan and New Zealand.
Ireland looked to hold the upper hand when Scotland finished on 187 for 8, having resumed at 56 for 1 after rain ruined Thursday's play. Mike Smith was their top scorer with 49 before becoming the first of two run- outs, and the 188 target looked well within Ireland's capabilities.
But the Scottish bowlers took advantage of the damp conditions to break down an Irish reply which failed to build any momentum, and they slumped to 141 all out.
Ireland never recovered from losing both openers with only 20 on the board, with the paceman Kevin Thomson taking both wickets. The slow left- armer Keith Sheridan weighed in with four wickets to account for the middle order, including the Irish captain and former Leicestershire player Justin Benson.
Alex Ritchie, general manager of the Scottish Cricket Union, said: "We have been inundated with calls and faxes from people congratulating us.
"It is marvellous. The players have worked so hard for this and I think they have proved a lot of people wrong. We were all a bit down yesterday after the rain interrupted the game but the boys obviously bowled and fielded really well today.
"I think it will be absolutely marvellous for Scottish cricket. It is a fairly tough group but we will do our best. It is something for everyone to aim for."
Scotland were quoted at 1,000-1 by bookmakers Ladbrokes and Corals to win the World Cup.
Gavin Craig, chairman of the Irish cricket union, said: "It is very disappointing to fall at the last hurdle, but let me salute a magnificent effort by Mike Hendrick and the squad.
"We have established a real reputation in the one-day game and I have no doubt we can reach the highest level.
"We are almost there already and we can only go one way from now on. We have already been invited to play in Kenya as a result of our ICC performance and I would expect other invites to follow."Reuse content