There is everything to play for between these two in Pool Two.
The Westerners trail Exeter by two points with French clubs Bayonne and La Rochelle out of the frame for the quarter-finals.
Former Ireland U21 out-half Gareth Steenson knows the Connacht they will encounter in Galway will be a different animal than the one that slumped 33-13 at Sandy Park in October. "I know the way they think.
"It's a big deal for them," voiced Steenson.
The Dungannon man followed a path to England where he spent two seasons at the Cornish Pirates before making his name at The Chiefs over the last seven seasons.
"It's a tough place to go and very windy, probably more windy than Sandy Park," voiced Steenson.
"It'll be vocal over there and they'll be looking to perform in front of their fans.
"We have gone well in this competition already this season, but so have they."
Exeter have shown the form in Europe that has recently eluded them in The Premiership where they have lost their last four rounds.
Connacht had taken on an aura of near invincibility until Edinburgh rocked up to Galway and wrecked their unbeaten home record last Friday night.
There are two ways it can go from here.
Connacht can recoil back into their expected place in the game as a perennial under-achiever.
Or, they can look for redemption.