Samoa ran in four second-half tries and five in all after captain Paul Williams touched down in the first-half for a commanding win in the first rugby Test at Mbombela Stadium, the 2010 football World Cup venue.
Wing Alapati scored his first Test try in his second game for Samoa in the 42nd minute, centre Johnny Leota pounced on an Italian error for a breakaway in the 53rd and number eight Tai Tu'ifua went over in the 64th.
Italy had a lone penalty by fly-half Luciano Orquera until a penalty try from a scrum in the 71st minute, before full-back Brando Va'aulu scored Samoa's fifth.
Samoa beat Scotland 27-17 in Durban last weekend and have two wins from two in the mini-tournament, which ends next weekend in Pretoria.
Warriors prop Euan Murray was also in action at the weekend but couldn't prevent Scotland going down 30-17 against South Africa.
His side delivered a hugely improved performance on the second game of their South African tour, but it was not enough to prevent defeat at the hands of the hosts.
The tourists produced a determined performance and led 10-6 at the break before the hosts overturned the deficit to secure a place in the final.
Murray and his side will now face Italy in Pretoria to try to avoid finishing last in the four-team tournament.