The defending champions set up an all-Irish final against Ulster at Twickenham on May 19, but only after Wesley Fofana had a try ruled out for Clermont in the final minutes.
Having trailed 12-6 at half-time in Bordeaux, Cian Healy's try early in the second half, coupled with a Rob Kearney drop goal and Jonathan Sexton's third penalty, saw Leinster close out the win.
Brock James converted five penalties from six attempts for Clermont, who threw everything at the Leinster line late on only to see Fofana's try ruled out by television match official Geoff Warren for a knock on.
Reflecting on reaching another Heineken Cup decider in his second year in charge, Schmidt said that out-half Sexton had made a key suggestion at half-time.
"Jonny Sexton spoke of course and called the play that we did right after half-time," said Schmidt.
"He said 'let's do this play, let's get it dead right and we'll score from it'.
"So anyone who doubted at half-time was pretty quickly in full agreement with Jonny when he knocked over the conversion (of Cian Healy's try) as well to give us a one-point lead.
"We also talked about the scrum and the lineout, making sure that we got the ball from those set phases, because we just felt if we could get some good quality we could put them under pressure, like we had done in the first 15 or 20 minutes."
Leinster captain Leo Cullen admitted it was among the toughest European games he had played.
"To be honest it was pretty intense out there. I think both teams made quite a few mistakes considering the quality of players out there," he said.
"I think a lot of it was to do with the pressure that was there as well. It was one of those games that could have gone either way.
"It goes to the TMO - sometimes you get them, sometimes you don't. We got it there today and at the end of the day that's the difference between the two teams."
Clermont Auvergne head coach Vern Cotter was obviously disappointed to see his side lose their first Heineken Cup semi-final in such dramatic fashion.
"When we were on top and didn't get a reward at the end, it's difficult. I think it'll take a while for us to get over this game," he said.
"The start of the second half was difficult for us. That's when they came back. We were six points ahead and they scored a try.
"We lost the lead and we were forced to change and to play differently."
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