Win handsomely and they had a chance to progress into the last eight as a best runner-up.
Premiership leaders Saracens, meanwhile, will qualify from Pool Three if they topple Allianz Park visitors Connacht on Saturday, but it is likely to be as a best runner-up, with Toulouse expected to win that group.
They were perhaps a little unfortunate Chad's withdrawal denied them the chance to qualify as a best runner-up, but they took only a point from two games with Egypt and could only draw away to Tanzania.
If Treviso are closing the gap on the other European powers, but Calvisano still look to be filling the role of whipping boys, with the other teams in Pool One looking to take advantage by boosting their try tallies in the race for a best runner-up spot in the quarter-finals.
Ian Humphreys intercepted a scruffy pass from a scrappy ruck to give Ulster a consolation try and cast a little light on their hopes to scrape through to the last eight as a best runner-up, but it was but a moment of inefficiency by Saracens to give away cheap score.
Last year the Blues alone made the quarter‑finals, qualifying from the pools as a best runner-up, and their dispatch there by Leinster – it was painfully undemanding for the defending champions – made no difference to the sense of well-being that went with another Welsh grand slam in the Six Nations.
Biarritz and Bourgoin both needed to win against Cardiff and Sale respectively to have a chance of claiming a best runners-up spot.
South African joy in Nelspruit and around the country turned to despair after the realisation that they could not qualify as a best runner-up either.
This time around, Marcos Paqueta's side surprised everyone when securing their passage despite political turmoil - eventually qualifying after a heroic defensive display in Zambia where a goalless draw was enough to take Libya through as a best runner-up.
Quins' defeat in Pool 6 also guarantees Ulster's passage from Pool 4. Brian McLaughlin's men face a tough match away to Clermont Auvergne on Saturday but now know their quarter-final place is assured, as even defeat will leave them with a best runners-up spot berth.
