Pienaar's coolly-struck collection of five penalties were vital in the end as the Scots had the final say, grabbing a converted try in injury-time which cut the gap to just three points.
But the hard work had been done by Brian McLaughlin's men who, helped by a superior set piece and another strong display in defence, will march on into the May 19 final at Twickenham.
Despite the deafening chants of 'Stand Up for the Ulstermen' inside the Aviva Stadium as this novel semi-final got underway, Edinburgh slightly edged the early exchanges until the concession of a sixth minute penalty on halfway.
Man-of-the-match Pienaar showed no evidence of early jitters as he slotted over the long range kick to perfection but Ulster's lead lasted less than four minutes as Greig Laidlaw equalised with a kick from a similar distance.
Edinburgh's top Heineken Cup points scorer, with a tally of 82 before the game began, stepped up again only moments later to kick his side ahead with another assured kick from outside the ten-metre line.
Ulster probed well straight from the restart, eventually forcing a five-metre scrum after neat play from Pienaar and Craig Gilroy.
Great work from Wannenburg at the base of the scrum, dribbling then picking up and diving for the line, sent the Ulster-dominated 45,147 attendance into raptures in the 16th minute. Pienaar converted his South African compatriot's score to move the Ulstermen 10-6 ahead.
Ulster tails were up, and a second try moments later was only prevented by strong Edinburgh tackling after Paddy Wallace had capitalised on a charge down to make a dash through the heart of the Scottish defence.
As the intensity increased, a try-saving intervention from Stefan Terblanche and good sweeping up by Pienaar, as Edinburgh's resulting five-metre scrum went awry, safeguarded the lead as the half hour mark approached.
The Scots were looking more and more dangerous, however, and the pressure increased further still as Terblanche was sin-binned in the 29th minute for an apparent slap on Edinburgh hooker Ross Ford, whom he felt was holding onto the ball too long in the tackle.
Ulster weathered the storm manfully and were even able to extend their lead while a man down, the ever-accurate Pienaar once again splitting the posts.
However, the first half ended on a sour note for the pre-match favourites as the hard-working Stephen Ferris was ruled offside in front of his posts and Laidlaw had little trouble nailing the kick for a 13-9 scoreline at the interval.
The Edinburgh captain had reduced the arrears to a solitary point within six minutes of the restart, but Ulster soon carved open a gap on the right as Darren Cave ran hard through midfield.
Cave tried to link with the onrushing Andrew Trimble out wide, but his pass was a difficult one for the winger to grasp and he duly knocked on.
Then came a moment of individual brilliance from Pienaar as he kicked and chased deep into Edinburgh territory, exerting so much pressure on receiver Tom Brown as to force the full-back out of play and earn an encouraging lineout well inside the visitors' 22.
As Ulster pushed and probed over the ensuing phases, both Dan Tuohy and Wannenburg found themselves in possession a matter of inches from the Edinburgh try-line, but both were held up by dogged defending.
With Edinburgh not budging despite the best efforts of the Johann Muller-led pack, Ulster had to settle for another three points from their period of dominance with Pienaar splitting the posts in the 59th minute.
A further Edinburgh infringement just four minutes later allowed the Springbok star to increase the lead to seven points, and Ulster came close to killing off the tie altogether as a trademark left wing burst from the electric Craig Gilroy tested out the Scots' rearguard.
The victory was confirmed in the 75th minute though, as more Edinburgh indiscipline at the scrum gave Pienaar the opportunity to land his fifth successful penalty - this time from straight in front of the posts.
As the clock ticked past 80 minutes Edinburgh finally breached the Ulster defence courtesy of replacement Jim Thompson, but Laidlaw's conversion was the final kick of the game and the celebrations could begin for London-bound Ulster.
Giving his post-match reaction, delighted hooker Rory Best said: "This is massive for Ulster Rugby. It has been talked about so much in recent weeks and the support has been immense.
"There is a group of us - Nigel Brady, Stephen Ferris, Declan Fitzpatrick, Paddy Wallace and Andrew Trimble - that have come through a lot of dark days and stuck around to try to get to an occasion like this.
"And the support we have all had has been absolutely fantastic. Right from the start of the day when we left the hotel, got on the bus, arrived at the ground and all through the day.
"The Ulster fans were like a 16th man to us. I'm delighted to be in the final, but credit to Edinburgh - they put it up to us and the game was in the balance right to the last minute."
Neither side played to its potential with Edinburgh left frustrated by their failure to score while Terblanche was off the pitch, and a series of unforced errors and poor decisions ruined some promising attacking moves for them.
Ulster racked up some big wins over Edinburgh in the league this season (42-20 away and 38-16 at home), but this was a much closer affair and their backs were not allowed enough room to find their rhythm in attack.
Out-half Paddy Jackson, making his first European start at the age of 20, acquitted himself extremely well in such a cauldron of pressure and he found a terrific touch for Ulster at a crucial stage in the second half.
Tighthead prop Fitzpatrick was another player who really stepped up to the mark. Having only recently returned from a five-month injury absence, he was part of a solid scrummaging unit and was a very able deputy for the suspended John Afoa.
The Ulster management will undoubtedly pick holes in their side's performance, yet McLaughlin is well aware that the result is all that matters in such a high stakes encounter as this.
Ulster are bidding to emulate the achievements of the province's 1999 European kingpins, and they are now just 80 minutes away from doing just that - they could yet face provincial rivals Leinster in the Heineken Cup's first ever all-Irish final.
|Ulster Rugby Score Card|
|Edinburgh Rugby Score Card|