The Toulon full-back booted six penalties and a conversion of wing Bryan Habana's interception try midway through the additional 20 minutes as Toulon triumphed 25-20 to book a Twickenham final appointment with fellow French heavyweights Clermont Auvergne on May 2.
Leinster gave as good as they got for most of the contest, with centre Ian Madigan kicking five penalties and flanker Sean O'Brien scoring a late try, but it was Madigan's pass that South African speedster Habana intercepted to see Toulon home.
Toulon, bidding to become the first team in 20 years of European knockout club rugby to win three successive tournaments, were pushed all the way by a Leinster side who delivered their best performance of this season's competition.
Ultimately, though, they were left to reflect on what might have been, conceding 13 points during extra-time after holding Toulon 12-12 after 80 minutes.
"As a professional rugby player, something like this is what you grow up dreaming of," said Halfpenny, who joined Toulon from Cardiff Blues last summer.
"You work hard day in, day out to be involved in the big matches, and the success and ambition of Toulon, I felt that I wanted to be a part of that.
"I was fortunate to be given the opportunity and it was a challenge I felt that I needed. To be rubbing shoulders with these guys, I can only feel it is helping my game.
"The intensity and physicality today was right up there with an international match. It was touch and go throughout and games sometimes are decided by very small margins.
"You could not switch off for one second and credit to the boys. The character they showed was immense."
Halfpenny was part of the Blues team that lost a 2009 semi-final penalty shoot-out against Leicester in Cardiff, and he added: "I did think of that and I thought 'here we go again'.
"But Bryan read that pass superbly and luckily we didn't have to go to a penalty shoot-out this time."
Toulon boss Bernard Laporte said: "I feel very relieved indeed. It was not easy, and we were a bit vulnerable.
"We made a lot of mistakes - on a better day we might have won the game by a bigger score - but we showed tremendous spirit.
"There are not many games at this level that you play during a season and it is the team that makes fewest mistakes that mostly comes out on top."
For Leinster, though, it was a case of what might have been as their hopes of reaching a fourth European final in seven seasons fell agonisingly short.
"The overwhelming emotion is one of pride," Leinster head coach Matt O'Connor said. "The effort the lads put in was fantastic and we are obviously incredibly disappointed to come second.
"Habana's intercept was the turning point - he is world-class - but the positive for us was the effort. It was second to none.
"A lot of people had written us off coming into this game but we will back ourselves to go anywhere and beat anybody."
And Leinster skipper Jamie Heaslip added: "It felt like a boxing match out there. There was nothing between the sides.
"We probably left opportunities out there in the first 40 minutes and they had a purple patch in the first 20 minutes of the second half, but we stood our ground.
"We always have an inner belief that if each player does their job, we are a good team and we can create situations to get some points."