Finland, who needed to win to advance, are eliminated.
Erazem Lorbek led Slovenia with 14 points.
Three free-throws from Shawn Huff reduced the deficit to ten and then Teemu Rannikko and Petteri Koponen both hit from downtown to make the loud Slovenian supporters nervous at 64-60.
Goran Dragic made the game safe though from the foul line.
“We played with a lot of discipline and very strongly for 32 or 33 minutes with good defence,” Slovenia coach Bozidar Maljkovic said after the game.
It was a close first quarter which Slovenia started the brighter, Edo Muric hitting a three to give the Slovenians a 5-0 lead, which was countered by a 6-0 burst from Finland ended with a bucket from Petteri Koponen.
An Uros Slokar three-pointer gave Slovenia a little breathing space at 14-10, but Sasu Salin hit back to cut the gap to two after the first ten minutes (14-12).
Finland’s Mikko Koivisto levelled the game at 14 to begin the second quarter proceedings, but a Jaka Lakovic inspired last three minutes saw Slovenia’s lead jump to double-digits at 34-24.
Finland were not able to match-up to Slovenia’s height inside, as they found easy looks to lead 42-28 at the interval.
Despite Slovenia’s seemingly comfortable advantage, the plucky Finns fought back. Six straight points from Tuukka Kotti reduced Slovenia’s lead to 54-48 at the end of the third.
It was a sluggish final stanza, where neither team got any rhythm early. Slovenia pulled away thanks to six straight points from Erazem Lorbek.
A Lakovic triple extended Slovenia’s lead to 63-51, the game looked as good as over.
Finland fought back but it was not enough.
“The thing that hurt us the most was probably our poor rebounding,” Finland coach Henrik Dettmann said.
Finland were out-rebounded 42-33.