Munster confirmed their status as the top side in Pool A, with a 41-0 thrashing of Caerphilly.
Also in Ireland, Llanelli conceded a first minute interception try by Neil Doak, that helped to condemn them to at 16-9 defeat by Ulster. The reverse that means they will not appear in the quarter-finals.
Edinburgh have beaten Neath to take second place in Pool A. The victory ensures a home draw for the Scots in the quarter-finals.
Despite defeat, Neath will still be in the last eight, and can still dream of Celtic League glory.
Meanwhile Glasgow pulled off an impressive home win over Connacht by 29 points to nine.
Celtic League results
Munster 41 Caerphilly 0
Ulster 16 Llanelli 9
Edinburgh 27 Neath 13
Glasgow 29 Connacht 7