Ulster beat Montpellier 27-16 on Friday, but failed to grab a crucial fourth try which would have guaranteed them a European Cup quarterfinal place.
The Irish province racked up a fifth win in five Pool Five matches to give them a seven-point lead over Leicester Tigers.
However, the English giants should close the gap with a win at group whipping boys Treviso on Saturday, before a potential pool decider at Welford Road against Ulster next weekend.
Ulster had looked in control, but never particularly comfortable in the first 40 minutes at Ravenhill against a Montpellier side which had lost six of their last seven matches.
Having slipped down 0-3 to a seventh-minute penalty from Eric Escande, Ulster were swiftly on top with two tries in three minutes.
Paddy Jackson’s accurate cross-field kick was calmly collected by flank Robbie Diack to dive over for his third career try in the tournament.
South African scrumhalf Ruan Pienaar kicked a difficult conversion from tight on the touchline for a 7-3 lead.
Pienaar added his team’s second try on 26 minutes after collecting his own kick ahead.
His simple conversion made it 14-3 but Ulster took their foot off the gas and ended up going in at just 17-13 in front at the interval.
Montpellier lock Robins Tchale-Watchou burst through for 14-8 with Escande adding the extras.
Pienaar and Escande then exchanged penalties before half-time.
A penalty apiece followed early in the second half before former All Blacks prop John Afoa barrelled through for Ulster’s third try just before hour mark.
Pienaar added the conversion for a personal haul of 17 points on the night but some dogged defence from Montpellier prevented Ulster from grabbing the bonus point try.
* In Friday’s other match, Scarlets beat Racing Metro 19-13 in Pool Four.
The result means Scarlets’ quarterfinal hopes stay alive for another day at least, after they stunned Racing at the Stade Yves-du-Manoir.
ASM Clermont Auvergne remain in the driving seat to qualify from Pool Four, with Harlequins hot on their heels ahead of Saturday’s mouth-watering match up at the Twickenham Stoop, but Scarlets are mathematically still in with a shout of a place in the last eight.
Young wing Kristian Phillips was their match winner, with his stunning solo score just past the hour handing them a six-point lead that they never relinquished.
Wales flyhalf Rhys Priestland picked up the Man of the Match award with an assured display that ended with a 14-point haul courtesy of four penalties from five attempts and the conversion of Phillips’ try.
British & Irish Lions stars Jonny Sexton and Mike Phillips stood out for Racing, with the scrumhalf grabbing his side’s early try, but the Scarlets deservedly stopped a run of six straight defeats.
Friday’s scores and scorers!
Ulster 27-16 Montpellier
Tries: Diack, Pienaar, Afoa
Cons: Pienaar 3
Pens: Pienaar 2
Pens: Escande 3
Racing Métro 92 13-19 Scarlets
For Racing Métro 92:
Pens: Sexton 2
Pens: Priestland 4