Connacht secured their BKT URC play-off place thanks to a 26-5 bonus-point win at Edinburgh, coupled with Ulster's loss at home to Glasgow Warriors.
Stuart Lancaster's side won eight of their last nine URC games to finish on 54 points.
They sit in sixth place and can be overtaken by Munster and Lions, but cannot fall further than eighth.
Ulster will hope that Munster fail to pick up any match points when they host the South Africans on Saturday night.
Shamus Hurley-Langton scored twice as Connacht finished their campaign with back-to-back victories, following on from last weekend's success over Munster.
Following a tight start to the game, the Irish side went 5-0 ahead in the 24th minute when Josh Ioane flew over in the corner following a neat breakaway.
Connacht celebrated a second try five minutes before the break. After building through the phases they managed to crash over the whitewash through Hurley-Langton (above), who went in under the posts.
And there was still time for the visitors to score another before the break too, Hurley-Langton was on the end of it once again and Sam Gilbert added the extras to make it 19-0 at the halfway point.
Connacht were threatening to get out of sight and added a fourth score midway through the second half, a chip and breakaway set them on the front foot and Matthew Devine was able to sail under the posts to help make it 26-0.
Edinburgh did get themselves on the scoreboard after 72 minutes though, Ewan Ashman got the first points after Duhan van der Merwe's break but it proved too little too late.
