|Elvis Evora was instrumental for Portugal, contributing 5 points and 4 rebounds without missing a shot|
Portugal stunned Hungary 66-57 on Thursday night to punch their ticket to the EuroBasket.
In beating the Hungarians for the second time in the Additional Qualifying Round, the Portuguese improved to 2-1.
The triumph also sealed a spot in the EuroBasket for Finland (2-0), who had won their opening two games against the Hungarians and Portugal.
The Hungarians (0-3) are eliminated because they have just one game left.
Joao Santos had 16 points and seven rebounds to lead Portugal on Thursday.
A pivotal stretch in the game occurred after Hungary jumped into an 8-5 lead almost four minutes into the contest.
Filipe da Silva drilled a three-ball for Portugal and the visitors went on to reel off 11 unanswered points.
Hungary battled back, and when Marton Bader sank two free-throws, the hosts drew level at 18-18.
At the end of the opening frame, Adam Hanga made one of two shots at the charity stripe and the hosts trailed 20-19.
Portugal, under new coach Mario Palma and looking to make it back to the EuroBasket for the first time since 2007, then took complete control of the game in the second quarter.
And they did it with their defense, limiting the Hungarians to just three points for the first eight minutes of the quarter.
Getting a balanced attack on offense, Portugal extended their advantage to 39-22.
With Hungary trying to chip away, Marton Fodor hit a shot from the arc to trim the deficit to 42-28 in the last minute of the second quarter.
Portugal kept the pressure on, though, with Jose Costa sinking a three-pointer 13 seconds later.
That gave the visitors a 45-28 lead heading to the changing rooms and also injected them with more confidence.
Hungary weren't about to give in and stormed back, with Hanga's three-ball 56 seconds before the end of the third quarter trimming the deficit to 52-45.
However, Portugal got a free-throw from Carlos Andrade and a lay-up from Costa to extend the advantage to 55-45 with 10 minutes to go.
Instead of keeping the momentum going, Hungary caved in at the start of the fourth quarter.
A Costa lay-up with 4:41 to play stretched the visitors' lead to 66-48.
Palma's team didn't score the rest of the way, and while Hungary reduced the arrears to nine, they got no closer.
Portugal won the battle of the boards, 46-38.
Costa was the only other player than Santos to reach double digits in points with 10, while Andrade had 11 rebounds to go with his six points.
For Hungary, Bader had eight points and 11 rebounds.
Akos Keller led the Hungarians with 12 points.
Hungary Head Coach Dzunics Braniszlav:
"I think the Portuguese team deserved this victory. It's simple: they played much better tonight than us. I can only congratulate them."
Portugal Head Coach Mário Palma:
"Tonight the Portuguese National Team wrote a brilliant page in its history.
I just want to express my gratitude to all of those who contributed to this success. First of all the Portuguese Federation and its President, who provided the team with full conditions to prepare well. Last but not least, the team members, especially the players who fully deserved to be in Lithuania due to their professionalism."
Portugal Captain José Costa:
"It's one of the happiest moments in my career; I've no words to express what I feel right now. Thanks to everybody who made this moment possible."