They now have 16 points with one game left to play, while Clermont are second on 14 and Exeter Chiefs and Bordeaux-Begles have 11 apiece.
The final round will see Steve Tandy's side travel to the Chiefs - flying high in the English Premiership - knowing victory will end a six-year wait for a place in the quarter-finals.
"It's a very difficult place to go," said Jones. "They are doing very well in the Aviva Premiership and doing well in this pool so from our point of view it's still wide open.
"To be honest, a lot was said about our record - we haven't lost to a French side at home for a long, long time. We've had a lot of ups and downs but that's a record we can hold on to now.
"It's very easy to put pressure on young players and expect them to be up there with some of these teams who have a lot of experience. These guys are performing beyond their years."
Ulster are also still in the hunt for the last eight, despite slipping to a 33-17 defeat at the all-conquering Saracens.
They host Oyonnax - with just one win so far in Pool 1 - in round six, needing a win to keep their knockout hopes alive.
Elsewhere in the Champions Cup there were wins at home for Munster and Leinster, who overcame Stade Francais 26-13 and Bath 25-11 respectively on Saturday.
However, Glasgow Warriors suffered a last-gasp defeat at Northampton Saints, while Benetton Treviso lost at Leicester Tigers and Scarlets were beaten by French giants Racing 92.
In the Challenge Cup, Newport Gwent Dragons booked their place in the last eight with a game to spare by beating Castres Olympique 31-18.
Jason Tovey shone at fly-half, converting all four tries and adding a penalty after Hallam Amos had got them off to a flyer, crossing over inside the first minute.
It represented a perfect return from injury, with the 21-year-old making his first outing since a shoulder problem forced him off against England at the Rugby World Cup.
"You think about it the night before and that's exactly what you want," said Amos. "It was a great break by Sarel (Pretorius) and a lovely ball by Jason Tovey.
"In rugby you will pick up injuries, though it's been tough watching the boys, but I can't ask for much more than that with my first touch back after three months."
Zebre completed a double over Worcester Warriors with their 22-15 away win, while Edinburgh overcame Agen 23-0 on Friday night.
And there were narrow away defeats for Connacht and Cardiff Blues, at the hands of Brive and Harlequins respectively, but both are still in with a shout of making the quarter-finals.
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