Tonga needed to win by 30 points to overturn their first-leg deficit and the difficulty of their task was compounded inside the first 20 minutes when lock Harrison Mataele and front row pair Siua Maile and Jethro Felemi were forced from the field through injury.
Samoa took advantage to gradually impose themselves on the game, soon taking the lead after capitalising on an error-prone Tongan lineout. Alamanda Motuga recovered a lineout steal well before Rodney Iona threw a clever cut-out pass for Ed Fidow to cross untouched.
Tonga were always physical in defence and enjoyed some good field position in the first half but struggled to string together enough phases to seriously test the opposition defence. And Samoa were able to cement their ascendancy just before the break, with a great break from Neria Fomai allowing Jonathan Taumateine to score his side's second try.
That extra bit of quality separated the sides at halftime and it took Tonga until early in the second half before they were able to put together double-digit phases.
They proceeded to dominate large stretches of the second spell and soon closed the gap through Jay Fonokalafi's try, with the substitute burrowing across the line after a strong carry from Ben Tameifuna.
That try further buoyed Tonga and a good spell of possession was soon rewarded with a second try, as Sione Tuʻipulotu cut the deficit to eight after an effective lineout drive.
The set piece was much improved for the Tongans in the second half and their chances of taking something from the match were enhanced when Samoan prop Tietie Tuimauga was sent to the sin bin.
But reduced to 14 men Samoa slowed down the game and soon sealed victory, with Stacey Ili finishing off a breakaway and Kalolo Tuiloma adding some gloss to the scoreline.
Tonga will still have a chance to earn a trip to France, now heading on a different qualification path that begins with a clash against the Cook Islands next weekend.