The Pro14 regular season concluded with Glasgow and Leinster topping the two conferences, securing an advantage heading into the knockout stage.
The Warriors got the result they needed against Edinburgh to top Conference A with second-placed Munster overcoming Connacht 27-14.
Tries from Sam Johnson, Ali Price, Niko Matawalu and Tommy Seymour secured a dominant 34-10 win against Edinburgh, which missed out on next season's European Champions Cup.
In the quarter-finals Munster will face Benetton Treviso, which defeated Zebre 25-11 away, while Ulster will look to follow up a narrow win over Conference B leader Leinster with victory against Connacht.
Debutant Marcus Rea scored his first senior try for Ulster to secure the bragging rights in a 14-13 triumph.
The big prize on offer elsewhere was qualification for the European play-off and Scarlets joined Ospreys despite a 34-32 defeat to Dragons.
Two bonus points were all Scarlets had to show for its efforts after a second-half collapse, Matthew Screech's 78th-minute try setting up Jason Tovey for the decisive conversion.
Ospreys will have home advantage for the play-off after pipping Cardiff Blues with a 26-23 away win in similarly dramatic circumstances, as Sam Davies dispatched a last-gasp penalty.
Cheetahs thrashed Southern Kings 61-25 in the day's other match.