The Blaugrana have not failed to make the last four since 2007 and are now bidding to become the first side to successfully defend the European Cup since AC Milan in 1990.
Lionel Messi opened the scoring from the spot only to see Antonio Nocerino silence Camp Nou when he slotted home just after the half-hour mark.
However, Messi notched his second penalty of the evening on 41 minutes before Iniesta, who has never lost a professional game in which he has scored, slotted home in the second half to seal Barca's progress to the last four for the fifth year in a row.
"We had to work hard but we are happy to be in another semifinal," the midfielder told TVE. "Being in a fifth consecutive semifinal means that things are going very well for us and that the team still has the ambition to get here.
"This team always shows its true colors."
Iniesta also saluted his colleagues for the way in which they maintained their composure after Nocerino's equalizer.
"With Milan, it's never over," he mused. "We knew that if Milan scored one more goal we would probably be eliminated. However, the match was for 90 minutes and we knew that we just had to take our chances when they came."
The World Cup winner added that he does not care whether Barca is paired with Chelsea or Benfica in the next round.
"I just want to play in the semifinals," he said. "That's what is important."
Meanwhile, Iniesta's teammate Thiago Alcantara admitted that he still cannot believe that he is playing alongside some of the biggest names in world football.
"It's an honor to be in the dressing room with these players, and to achieve these kind of objectives," the 20-year-old midfielder confessed. "I am really happy to be at this club. I think we played a very good match and we deserved to win it."
Barcelona is bidding to become the first side to successfully defend the Champions League and has now equaled Real Madrid's all-time European Cup record for consecutive semifinal appearances.
Los Blancos won the first five tournaments between 1955 and 1960. Barca's semifinal win, meanwhile, started during the 2007-08 Champions League and the club has gone on to lift the title on two occasions, in 2009 and 2011.
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