Ulster secured a European Champions Cup quarter-final spot with a 22-15 defeat of Bath, while Northampton Saints and Glasgow Warriors stayed in the hunt for qualification on Saturday.
Clermont Auvergne sealed top spot in Pool 3 with a 26-19 victory at Harlequins, but Ulster knew a defeat of Bath would see them through as one of three best-placed runners-up.
The Pro14 side got the job done in the second half after the two sides were level at 7-7 at the break, Robert Baloucoune and Will Addison going over to add to a first-half try from Marcell Coetzee before Billy Burns was on target with a penalty.
Tries from Ruaridh McConnochie and Ross Batty, who was later red-carded for a no-arms tackle on John Cooney, were not enough for Bath to end the competition on a high note.
Northampton did all they could to advance as runners-up with a 36-24 victory at Top 14 high-flyers Lyon in Pool 1.
The Saints will go progress if either Saracens or Gloucester fail to pick up maximum points wins on Sunday after Mike Haywood, Teimana Harrison, Cobus Reinach, George Furbank and James Fish touched down in a bonus-point triumph at Matmut Stade de Gerland.
Glasgow must hope defending champions Sarries, whose relegation from the Premiership at the of the season for persistent salary-cap breaches was announced on Saturday, and Gloucester slip up after demolishing Sale Sharks 45-7 in Pool 2.
Leone Nakarawa set the tone early on with one of six Glasgow tries at the AJ Bell Stadium, where Adam Hastings scored 15 points from the tee.
Leinster made it six victories out of six in Pool 1 with an 18-0 defeat of Benetton Treviso, while Sam Simmonds grabbed a double as Pool 2 winners Exeter Chiefs saw off La Rochelle 33-14 at Sandy Park.
Beleaguered Sarries host Racing 92 on the final day of pool matches reeling from the announcement that they will drop of out of the Premiership, while Gloucester travel to Toulouse.