Lemi also became the all-time Pacific Nations Cup try scoring record holder. His two tries took him one clear of All Black Hosea Gear - the younger brother of former Warriors ace Rico Gear - on nine tries.
"Both teams gave it their all today," said coach Betham. "The last few minutes were very competitive as Fiji never gave up, so I am very proud of my players."
Lemi agreed with his coach adding: "Hopefully we can use this as a base and raise our level for next week's game against Japan."
Played under perfect conditions in the nation's capital, Samoa and Fiji combined for six tries in the opening game of the double header.
Following an early exchange of penalties between Setareki Koroilagilagi and his Samoa counterpart Ki Anufe, Fiji got the try fest going with Nemia Kenatale going over in the 10th minute as the Fijians launched a counter-attack from deep in their own half.
Koroilagilagi added the extras as Fiji went 10-3 up.
A second exchange of penalties followed before two scintillating tries in the space of two minutes saw Samoa take the lead.
Ben Masoe scored the first in the 27th minute following a well-judged kick from Lemi, before Paul Williams, Paul Perez and Faatoina Autagavaia combined to put Lemi away in the corner as Samoa went into the break leading 18-13.
The second half saw both sides look to play expansive rugby though handling errors from both teams meant it wasn't until the 50th minute that Lemi extended his side's lead.
A third exchange of penalties followed before Netani Talei's try in the 73rd minute closed the gap to five.
Anufe's fourth penalty of the day secured the win but Tuapati Talemaitoga's late try ensured the Fijians left Tokyo with a bonus point.