Exeter have joined Gloucester and the Dragons in the Challenge Cup quarter-finals after their 33-24 win at Connacht yesterday.
The Chiefs sit top of Pool 1 with 20 points and, although the Irish can level with them next week should they record a bonus-point win at La Rochelle while the Devon side fail to record a point against Bayonne, Exeter will remain top thanks to their two wins over Connacht.
The Chiefs trailed 17-10 in Galway as Matt Healy, Willie Faloon and Dannie Poolman all crossed for the Irish to counteract a penalty try awarded to the Chiefs.
But two second-half tries from Dean Mumm and Don Armand added to 13 points from the boot of Henry Slade saw the Chiefs clinch it and even deprive the home side of what would have been a vital losing bonus-point.