The visitors to the AJ Bell Stadium had already sealed their progress to the knockout rounds, but it was Sale who won the shootout for top spot to earn home advantage in the last eight.
They were given a helping hand on their way into the lead when Hallam Amos was sent to the sin-bin for a deliberate knock-on after just 11 minutes, allowing Danny Cipriani to open the scoring with a simple penalty.
The first try arrived not long after as prop Brian Mujati went over, and just six minutes later the hosts added another as the scrum proved too strong for the Dragons and the referee awarded a penalty try.
Sale continued to pile the pressure on the Welsh outfit and were twice held up over the line before registering their third try on the stroke of half time when Josh Beaumont peeled off the back of a scrum from just five metres out.
A bonus point arrived early in the second half when a moment of magic from Cipriani opened up the defence before he found Nev Edwards to go over in the corner, opening up a 31-point gap to all but put the game to bed.
Newport did finally get on the scoreboard shortly before the hour mark when Adam Hughes's half-break released Ashton Hewitt to go over, but the conversion was missed to leave the deficit at 26 points.
The final say went to the hosts, however, as Mike Haley went over for a fifth try in the closing stages to wrap up the comfortable victory and join fellow English sides Harlequins and Gloucester Rugby in the quarter-finals.