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 semi-final," the midfielder told TVE.
"Being in a fifth consecutive semi-final 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 colours [in such games]."
Iniesta also saluted his colleagues for the way in which they maintained their composure after Nocerino's equaliser.
"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 are paired with Chelsea or Benfica in the next round: "I just want to play in the semi-finals. That's what is important."
Meanwhile, Iniesta's team-mate Thiago Alcantara admitted that he still cannot believe that he is playing alongside some of the biggest names in world football.
"It's an honour 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 are bidding to become the first side to successfully defend the Champions League and have now equalled Real Madrid's all-time European Cup record for consecutive semi-final appearances.
Los Blancos won the first five tournaments between 1955 and 1960. Barca's semi-final win, meanwhile, started during the 2007-08 Champions League and they have gone on to lift the title on two occasions, in 2009 and 2011.
Between November and February, Goal.com published 10 exclusive extracts from Graham Hunter's highly anticipated new book, 'Barca: The Making of the Greatest Team in the World'. Click here to read all 10 extracts. Don't miss it!