Jones' troops soared into a 24-point lead at the Stade du Hameau by half-time as Cory Hill, Ashton Hewitt and Jason Tovey all crossed.
Tovey was metronomic with the boot, collecting 19 points in total, and Carl Meyer's early try in the second half wrapped up a bonus-point 34-17 win despite a late Pau surge.
It leaves the Dragons - who reached the semi-finals last year - two points clear of second-place Sale Sharks in Pool 2 with two games to go.
"We were a team, they had a lot of good individuals but we were by far the better side and deserved to come away with the spoils," said Jones.
"They brought all the big guns in and we were a bit apprehensive but we kept Colin Slade quiet, took their threats away, made them play and they couldn't deal with us.
"Good players get turned on by the big challenges and we faced that in Pau. We fully deserved what we got, our kicking game was outstanding and we took our chances when they came.
"We enjoy the tournament and I just hope we can get another victory to qualify and two more to get a home draw."
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