The Stormers will play the defending champion Bulls in the Johannesburg township of Soweto in just the second all-South African final in Super rugby history.
Center Juan de Jongh sent the Stormers on their way to victory with the game's only try, his first in Super rugby, when he sidestepped three players midway through the first half.
Stormers flyhalf Peter Grant kicked 20 points, including four second-half penalties to seal victory for the Cape Town team.
The competition's best defensive outfit did not concede a point for the final 55 minutes, after Berrick Barnes' 25th-minute drop goal.
Two Grant penalties gave the Stormers a 6-0 lead inside 12 minutes.
But Australia international Barnes landed a 16th-minute penalty, and then booted a long-range drop goal to put the Waratahs level in a tightly contested first half.
The game's defining moment came just a minute after Barnes' drop goal when de Jongh broke through the Waratahs backline, and stepped past fullback Kurtley Beale and wing Drew Mitchell for his first try in the competition.
The Stormers then kept the Waratahs out with another impressive defensive effort, underlining their status as the team with the best defense in the competition - they have conceded 177 points in 14 games, an average of just 12 points a game.
Grant punished the indiscipline of the Australian team with his four penalties in a 16-minute spell in the second half, sending the Stormers to a first Super rugby final after semifinal losses in 1999 and 2004.
The last Super 14 final - the competition increases to 15 teams next year - is set for next Saturday at Soweto's Orlando Stadium.
Soweto has become the Bulls' temporary home after they handed over their regular Loftus Versfeld stadium for the football World Cup.
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Scores:
Stormers 25 (Juan de Jongh try; Peter Grant 6 penalties, conversion), New South Wales Waratahs (Berrick Barnes penalty, drop goal). HT: 13-6.
