Ahead 16-3 at half-time, the Munster pack laid the foundation for a famous victory which included later tries from Ronan O'Gara, who scored 20 points, and Trevor Halstead.
O'Gara described the victory as "unbelievable" and he is now looking forward to making it third time lucky in the Heineken Cup final - and eradicating the memory of their 15-9 defeat against Leicester Tigers at the Millennium Stadium in 2002.
"Unless you're in our dressing room, you don't know what it means to us," he said. "We have a huge tradition and pride in where we come from.
"Getting up for today wasn't going to be a problem. If we'd lost today, it would have been very difficult to walk the streets tomorrow. We didn't want to let anyone down and it's a proud day for us.
"Credit to our coaching staff ... to hold Leinster tryless on the biggest day in Irish rugby is incredible.
"We have huge respect for Leinster, but we'll enjoy the next day or two and have a good night or two.
"The hard work begins now. We've been to two finals and we haven't produced the goods yet. Biarritz are the sleeping giants of this tournament - they've been cruising in third gear and beating teams."
Man of the match Paul O'Connell, who was at the heart of the mighty Munster forward effort, warned that nothing has been achieved just yet. Becoming champions of Europe is now the main focus.
"Things went our way today. The bounce of the ball went our way and not Leinster's," he said. "We played some good possession rugby. We retained the ball well and defended very well against a world-class backline.
"You always need a bit of luck in this competition. Players, coaches and fans know that this isn't the pinnacle for us - there's got to be something left in the tank."
For Biarritz it will be a first trip to the Heineken Cup final having fallen at the semi-final hurdle in the past two seasons. They held out Bath in a game in which all the points came from the boot in San Sebastian.
French scrum half Dimitri Yachvili made it third time lucky for his side a 100% goal kicking that included five penalties as the Basque outfit won 18-9.
Having missed out to French rivals Toulouse and Stade Francais Paris in the last two semi-finals, Yachvili and co thrilled the packed Basque crowd at Estadio Anoeta in San Sebastian with a power packed display that guaranteed them a ticket to Cardiff.
"We are very proud to reach the final because it is a first for us - and because we missed out in the last two semi-finals," said Yachvili. "All our fans are proud of our achievement and we will now do everything we can to bring the Heineken Cup back to Biarritz and the Basque country."
Having beaten two of England's top sides in the knock-out stages, Sale Sharks and Bath, Yachvili said he didn't mind which one of the two Irish sides Biarritz met at the Millennium Stadium.
"We felt in control of the game, but less so than we did in the quarter-final against Sale. We knew Bath would be strong up front and they didn't disappoint us," said Yachvili. "We just played the match we had to play to win and we will do the same in the final. If we have to play like we did against Bath to win, then that's what we will do."