Now the final battle is to be the best of the qualifiers with Gloucester Rugby on 22 points and London Wasps on 21 home and dry with Stade Francais Paris, Worcester Warriors and Perpignan all on 20 points.
Prop Paul James got their only try with Tom Heathcote contributing the rest of the points with the boot - and now Bath end their group campaign at home to Bucharest Wolves on Saturday with 29 match points their target.
"We definitely want to follow it up with another win," said head coach Gary Gold.
"It's a big issue because obviously the teams that don't get that top seeding play the three Heineken Cup teams that come down. We want to do as well as we can and in doing so it makes sense to make life as easy as possible for ourselves when we can.
"With what's gone on in the last couple of weeks and how disappointed we've been, it's good to come away with a win and give ourselves a home qualification in the quarter-finals," said head coach Gary Gold.
"I'll take the positives but I don't want to cover over the fact that we've got to set ourselves standards that are higher than that.
"I think there were opportunities in the first half when we could have closed the game out. We had more than enough opportunities and should have had better reward when we visited their 22 on a couple of occasions.
"We panicked a little bit, we just have to hold onto the ball and look after it. We needed to keep our composure and keep exerting the pressure."