The win put Kenya on course to defending the Singapore title they won last season.
Gordon Langkilde put Samoa ahead with a converted try before Amonde weaved through the Pacific Islanders defence to draw Innocent Simuyu's charges level at the stroke of half-time.
Second half tries by Billy "The Kid" Odhiambo and Nelson Oyoo helped Shujaa see off Samoa, although the Islanders were undone by two yellow cards to their players in a span of two minutes.
With Australia hitting Argentina 19-7 in their last group stage match, Kenya advanced to the Cup quarters, their second time this season after Cape Town in December, alongside the Aussies who topped the pool with a 100 percent record.
Earlier, Kenya Sevens had beaten Argentina 22-7 before losing to Australia 29-7.
Nelson Oyoo scored Shujaa's only try against the Aussies.
Shujaa got their defence off in style when Frank Wanyama scored a try in each half to propel them to victory over Santiago Gomez's Pumas.
Unconverted tries from Wanyama and Oyoo gave Shujaa a 10-0 lead at the breather before Dennis Ombachi scored after the restart to stretch the lead to 15-0.
Skipper Andrew Amonde would weave through before offloading to Bush Mwale who set up Wanyama for his second try of the game. Brian Tanga's conversion put the defending champions 22-0 up.
The Argentine grabbed a late consolation through Nicolas Menendez' converted try. The other Pool C encounter saw Australia edge Samoa 19-12.