They got there at the expense of Great Britain, who play Japan this afternoon. The 25-15 25-16 25-13 win takes Dominican Republic four points clear.
They have been slow burners in the tournament after starting with two defeats but found their rhythm when it mattered and will now carry some hope in to the last eight.
In Brenda Castillo they have the tournament's best libero and with a tall front-row at their disposal, they have the game and the flamboyance to trouble the favourites.
Prisilla Altagracia Rivera Brens topped the scoring with 21 points today, while the ever-reliable Milagros Cabral de la Cruz chimed in with 14.
Speaking after the match Rivera Brens said her side was confident they could win and did not rule out their chances of winning a medal. 'The ball is round so everything is possible.'
A last-eight clash with the USA beckons, while Algeria will head home with just a set to their name after a disappointing tournament.
Bethania de la Cruz de Pena ended as the Dominican's top-scorer over the group stage with 67 points, with Zohra Bensalem (55) taking that honour for Algeria.