Bath needed a bonus-point victory to ensure a home quarter-final, and Stephenson's second try in the opening minute of the second half secured it against a French club no longer interested in the tournament.
Bath will play Guinness Premiership front-runners in early April for a place in the final four and coach Steve Meehan is looking forward to the match.
He said: "That's a very important game for us. We haven't been looking at this tournament in terms of trophies, but I'd love to see the players win it.
"They've worked very hard and they've been bridesmaids too many times, but as the cliche goes, we'll take one match at a time. I was very, very happy with today's performance."
In Italy, winger Ollie Phillips scored a try double as the Falcons gave Petrarca a rugby lesson in their 50-6 victory.
Needing a bonus-point victory to make the Challenge Cup quarter-finals, Newcastle had it wrapped up by halftime, with Phillips completing his brace in only the 12th minute.
Young fly-half Toby Flood got into the action with a try to go with his five conversions, and the result was never in doubt as the visitors ran in eight tries in all.
The win sneaked the Falcons into the final eight as the last qualifier, and they face a tricky trip to French heavyweights Clermont Auvergne in the next round in April.
Worcester replacement Thinus Delport bagged a brace of tries in his side's 19-16 win at Viadana, but couldn't prevent the Warriors being knocked out of Europe.
Worcester needed a bonus-point victory in Italy to keep alive their slim hopes of making the quarter-finals, but came up against a gritty Viadana side who refused to buckle.
Harlequins are also out, but finished their European campaign with a flourish as they saw off Connacht 26-10 at the Stoop.
Narbonne beat GRan Parma 54-12 in the evening game to complete the Pool stages.