Baker scored two tries in the semifinal victory and, with his try in the final, increased his all-time try-scoring record for the United States to 158.
"Some of the emotions have gone to my head right now, singing that national anthem with everyone", USA captain Ben Pinkleman said.
The hosts had ousted Fiji 19-7 in the semi-finals, as Argentina stunned defending champions and current series leaders South Africa 12-10 with a late Renzo Barbier try and conversion by Gaston Revol. "That truly was such a moving moment and then to be able to come out and perform the way we did. was surreal".
"We just knew this was our moment".
The Fijians will play the undefeated United States, who beat England 17-12 behind Perry Baker's three tries.
Kenya staged a comeback as they scored converted tries through Samuel Oliech, who later left the match injured, and William Ambaka Ndayara who level the scores.
The Springboks also scored four tries but they failed to convert three which made the difference.
However, despite their fourth place finish, the Blitzboks still remain well in the lead of the World Series standings with their 92 points trumping log-second New Zealand, by ten points.
Coach Gareth Baber said the target was to keep improving on the field and also on the points table.
By scrapping their way through Pool B against Wales‚ Canada and England and then beating Australia in the quarterfinals in Las Vegas‚ the Blitzboks were on track to meet Powell's objective.
Argentina and the US progressed to the Cup Final, which saw a 28-0 victory for the Americans.
The innocent Simiyu led charges must now beat Fiji in their last pool match to stay in the race for a third main cup quarter final appearance.