Wing Kotaro Matsushima crossed in the corner to seal the five-point haul as the hosts moved to the top of Pool A and set up what will likely be a winner-takes-all tussle with Scotland in Yokohama, where Japan can seal a first-ever World Cup quarter-final place, on October 13.
"I feel a little bit relieved," Joseph told reporters. "I thought Samoa played really well, to bring a physical performance like that after they played a few days ago against Scotland, they should be very proud.
"We were a bit frantic in the first half, we didn’t execute exactly how we wanted to, but after halftime I thought we were more in control."
It looked as though the extra point would elude Joseph’s side but they then snatched two last-gasp tries, the first coming in the 75th minute and Matsushima's score following five minutes into extra time.
"Our team has incredible belief to the very end and the bench came on and made a massive impact on the game," Joseph said.
"That is one of the big reasons why we have been successful. It is not just one or two players that we rely on."
Japan have now won three games at the World Cup for the second time in their history, repeating the feat of 2015, and Joseph added that they now have confidence that the can seal a place in the last eight, in contrast to four years ago.
"Even today, the belief in our team has grown and I guess we'll need it going into next week. It’s the first time ever Japan's got themselves in the position where they can top the pool, so it's new territory for us.
"Scotland are a very good team with a lot of experience and x-factor. We saw how clinical they were against Samoa [in a 34-0 win].
"I think it was always going to come down to the Scotland game. It’s going to be a ripper. I can’t wait and the players can’t wait."