An eight-try demolition of Oyonnax this afternoon at the Kingspan Stadium gave Ulster their best possible chance of progress into the last eight of the European Rugby Champions Cup, with the victory, four-try bonus point and final pool points differential of 60 applying intense pressure on their Round Six rivals.
Les Kiss' side finish second in Pool One on 18 points, but must now wait for results from elsewhere before a quarter-final place can be confirmed, with essentially six other teams vying for five remaining slots.
With Saracens, Racing 92 and Leicester Tigers already through to the next round, Ospreys, Clermont Auvergne, Northampton Saints, Stade Francais, Toulon and Wasps are all still in contention, so Ulster must wait in hope that their 18-point haul and strong points differential will guarantee qualification as one of the best three runners-up.
Oyonnax offered little resistance this afternoon, as scores from Rob Herring, Darren Cave, Rory Scholes and Sean Reidy secured the bonus point before half-time, while Craig Gilroy, Robbie Diack, Ian Humphreys and Jared Payne topped up the score after the break - all the tries going converted, five by Paddy Jackson and three by Humphreys.
With Ruan Pienaar unavailable for selection due to illness, Stuart McCloskey rested and Rory Best starting on the bench, the Ulster lineup was nonetheless bolstered by the return of Cave, rehabilitated from a shoulder injury sustained in December, and Nick Williams, victim of a concussion in the away leg two weeks ago.
Cave teamed with Six Nations squad selectee Luke Marshall in the centre, in front of a back three of Payne, Andrew Trimble and Gilroy, with Paul Marshall taking over from Pienaar at scrum-half, alongside Jackson at 10.
Herring - another inclusion in Joe Schmidt's squad - took over hooker and captain duties from Best, propped by Kyle McCall and Ricky Lutton, with Alan O'Connor and Franco van der Merwe continuing in the second row, and Williams joining Diack and Reidy at the back of the scrum.
Ulster wasted no time from the off, Diack charging down an attempted clearance kick in the Oyonnax '22' and, as the Frenchmen impeded while scrambling to defend, the rolling maul off the lineout saw Herring bundle over with barely three minutes on the clock.
Jackson's conversion dispatched, a Rory Clegg penalty got Oyonnax on the scoreboard before Ulster's next surge, with a high tackle setting exactly the same scenario as that from which Herring had scored 10 minutes before.
However Ulster crossing put paid to any prospect of points, until minute 18 when Williams marauded forward with three tacklers hanging off his hulking frame, then fed Payne who supplied Cave for a neat try, converted once again.
With Clegg squandering a 23rd-minute penalty, ruthless Ulster showed no quarter, with replacement Scholes bagging try number three with his first touch after coming on as a blood replacement for Trimble. Strong, pacy running from Payne and Luke Marshall set up the score, with Jackson supplying the final assist before adding the extras.
Williams came close to securing the bonus point as early as the 33rd minute as he barged from the back of a rolling maul only to be held up over the line, but the breakthrough was not much longer in coming, Reidy touching down a minute before the break after good ball shielding in the maul from Paul Marshall.
Half-Time Score Ulster 28 Oyonnax 3
More of the same from Ulster as the second half opened saw Gilroy touch down in the corner on 47 minutes after more enterprising work from Luke Marshall and rapid-fire passing between the backs, before a great take of a difficult low ball by Payne made possible try number six, awarded to Diack after a long consultation between referee Marius Mitrea and the TMO.
Humphreys, recently entered in place of Jackson, put over the conversion and was soon adding another seven individual points, exposing a central gap inside the Oyonnax '22' and grounding under the posts.
Cave and Payne combined on the hour mark for try number eight - which the full-back's work-rate throughout the match had thoroughly deserved - and with Jackson back in the fray for the final 10 minutes after Humphreys had found himself on the end of a bonecrushing tackle from Maurie Fa'asavalu, Ulster pressed on in the quest to raise their points difference further still.
It proved not to be - even with newly-appointed Ireland captain Best coming into the ranks for the final minutes to a rapturous ovation - but Kiss must be satisfied that his side have given their absolute best, and will observe the unfolding drama of the final weekend with much interest.
Full-Time Score Ulster 56 Oyonnax 3
Ulster (15 - 9) Jared Payne; Andrew Trimble, Darren Cave, Luke Marshall, Craig Gilroy; Paddy Jackson, Paul Marshall
(1 - 8) Kyle McCall, Rob Herring (c), Ricky Lutton, Alan O'Connor, Franco van der Merwe, Robbie Diack, Sean Reidy, Nick Williams
Replacements (16 - 23) Rory Best, Callum Black, Bronson Ross, Clive Ross, Roger Wilson, David Shanahan, Ian Humphreys, Rory Scholes