Bezuidenhout's 24-point haul sealed the deal
Flyhalf Carl Bezuidenhout was the star performer for the hosts as the pivot ended with a personal haul of 24 points - courtesy of five penalties, three conversions, and a drop-goal.
The result means the Pumas will host either the Golden Lions or Western Province in the Final on May 18.
The hosts took an early lead when Bezuidenhout succeeded with a close-range drop-goal.
The flyhalf then nailed three penalties before the hosts scored their first try, when hooker Frank Herne set off on a 25-metre run down to the right-hand touchline, before off-loading to left wing Rosko Specman, who sprinted clear for a converted try.
The Kings salvaged something from a disappointing first-half when flank Mpho Mbiyozo was mauled over for a converted try with two minutes left.
Bezuidenhout and his opposite number Wesley Dunlop traded penalties after the restart to leave the score 22-10 in the Pumas' favour. Dunlop cut the deficit to just nine points with a 61st minute penalty.
Two minutes later the Pumas squashed any hopes the Kings' had of mounting a fightback, when fullback Coenie van Wyk sniped over in the left-hand corner for a converted try.
Bezuidenhout then slotted his fifth penalty of the game before right wing JW Bell left the Kings' defence in tatters, when he set off on a 25-metre run which resulted in a converted try four minutes before the end of the match.
For the Pumas:
Tries: Specman, Van Wyk, Bell
Cons: Bezuidenhout 3
Pens: Bezuidenhout 5
For the EP Kings:
Pens: Dunlop 2
Pumas: 15 Coenie van Wyk, 14 JW Bell, 13 Wilmaure Louw, 12 Stefan Watermeyer, 11 Rosco Speckman, 10 Carl Bezuidenhout, 9 Francois de Klerk, 8 Renaldo Bothma, 7 Jaco Bouwer, 6 Corne Steenkamp (captain), 5 Eduan Van Der Walt, 4 Uzair Cassiem, 3 Ivann Espag, 2 Frank Herne, 1 Vincent Koch.
Replacements: 16 Jacques Momberg, 17 Corné Fourie, 18 De-Jay Terblanche, 19 Marius Coetzer, 20 RW Kember, 21 Jerome Pretorius, 22 Dewald Pretorius.
Eastern Province Kings: 15 Kayle van Zyl, 14 Brian Skosana, 13 Wayne Stevens, 12 Tiger Mangweni, 11 Michael Killian, 10 Wesley Dunlop, 9 Scott Mathie, 8 Paul Schoeman, 7 Mpho Mbiyozo (captain), 6 Tomàs Leonardi, 5 Darron Nell, 4 Stefan Willemse, 3 Charl du Plessis, 2 Coenraad Britz, 1 Lizo Gqoboka.
Replacements: 16 Dane van der Westhuyzen, 17 Ross Geldenhuys, 18 Samora Fihlani, 19 Dalton Davis, 20 Dwayne Kelly, 21 Marlou van Niekerk, 22 Lonwabo Ntleki.
Referee: Tiaan Jonker
Assistant referees: Ben Crouse, Stephan Geldenhuys
TMO: Johan Greeff