Pisi crashed over for three tries during a second half in which Saints scored 20 unanswered points to down the Men in Black.
Will Hooley's two early penalties rewarded a strong start from the hosts. But Saracens fought back well, Ben Ransom scoring the first half's only try to give the visitors a 7-6 half-time lead.
It could have been more, Marcelo Bosch having a score notched off after a forward pass earlier in the move and Jamie George conceding a penalty within sight of the home whitewash.
After the break Saints punished this profligacy, with Stephen Myler adding a conversion and a drop goal to Pisi's trio to send their team to Sandy Park for next Sunday's final.
And while Pisi acknowledged that the game ranked up their with his best in the black, green and gold, he also paid tribute to the forwards for laying the foundations for him to score.
"It's up there with them, but it's credit to the forwards," the Samoan told SaintsTV. "They grafted in the first half and we were a bit loose in the first half. Then in the second half we went back to basics a bit, the forwards went forward and we're happy to get the glory!
"We started quite well but a few balls went loose. But we knew if we were patient the points would come."
Following the Wanderers' Aviva 'A' League final appearance in December and the Under-18s' Premiership Rugby Academies League title-winning campaign in January, next Sunday marks the first time the first team can bring home a trophy this season, with Pisi adding: "Getting to play for silverware is good for us.
"It's one of three competitions that we're in and hopefully we can go all the way."