Paris: Ulster beat Montpellier 27-16 on Friday but failed to grab a crucial fourth try which would have guaranteed them a European Cup quarter-final place.
The Irish province racked up a fifth win in five Pool 5 matches to give them a seven-point lead over Leicester.
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 3-0 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 lock forward Robbie Diack to dive over for his third career try in the tournament.
South African scrum-half 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 the night`s other match, Scarlets beat Racing Metro 19-13 in Pool 4
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