The French Top 14 pacesetters dominated their Irish opponents in the first half but failed to capitalise, giving Munster hope in a nail-biting finale but the hosts prevailed.
Clermont, who will play either Saracens or Toulon in the final on May 18 in Dublin, triumphed courtesy of Nalaga's early try and Parra's conversion and three penalties.
Double Heineken Cup champions Munster scored from a Denis Hurley try and Ronan O'Gara's conversion and penalty.
Saracens will meet Toulon in the second semi-final at Twickenham on Sunday (1400 GMT).
Clermont, the only team to have won all seven previous games in this season's competition, quickly moved 10 points clear before Munster produced a typically gritty performance.
Beaten 19-15 in last year's semi-finals by eventual champions Leinster, Vern Cotter's team survived this time.
"We almost conceded a try just before the interval but we did not crack," said Clermont captain Julien Bonnaire. "I think it was the turning point of the game, we held firm on our line."
Munster coach Rob Penney added: "Clermont have an exceptionally talented style. They're just fantastic athletes. Defensively that's really tough. We had opportunities and it could have been a different story had we taken them.
"Looking back there will be some frustration, but right now I couldn't be prouder."
O'Gara's penalty put the visitors ahead early on but Munster were soon under pressure, conceding a try in the eighth minute.
Wing Nalaga had three players on his outside but decided to cut in and went over on his own before Parra slotted home a routine conversion.
Parra added two penalties to give Clermont a comfortable lead as Munster looked breathless after only 15 minutes.
The Irish were lucky to reach halftime only 10 points down, with Clermont twice going close to crossing the line, although the visitors almost scored themselves just before the break.
Munster were on the attack early in the second half but it was Clermont who scored first as Parra continued his perfect kicking run with a third penalty.
With Wesley Fofana and Sitiveni Sivivatu in a class of their own, Clermont continually put Munster under huge pressure.
The Irish side got back into the game on the hour when Hurley collected O'Gara's clever through kick and touched down and O'Gara converted.
With Munster breathing down the French team's neck, Parra missed his first kick and the pressure was suddenly on Clermont's shoulders.
An unkind rebound behind his line fooled Nalaga and the ball presented itself for Felix Jones to grab and touch down but the fullback knocked on, wasting his side's last chance of an upset in their 10th Heineken Cup semi-final.
"We spent enough time in their 22, especially just before halftime and a good few times during the second half. We just haven't converted enough during the season and today. It was a tough game," Munster captain Paul O'Connell told reporters.
- Sports & Recreation
- Heineken Cup