Connacht's recent winning streak was ended by Glasgow Warriors after a narrow loss at at Scotstoun last night.
It finished 29-27 to the home side.
Andy Friend's side, who travelled to Glasgow after winning six on the bounce in the URC, will travel to Ulster in the last eight on the weekend of 5/6 May.
The URC quarter final line up has been confirmed.
Leinster will take on Sharks and Ulster face Connacht.
Munster will be away to Glasgow and Stormers go head to head with Bulls.
The ties will be played on the weekend of the 5th, 6th and 7th of May.