Marland Yarde was the star performer with a hat-trick of tries while Halani Aulika collected a brace of scores, Alex Gray crossed over one and Tom Homer kicked 16 points in a deserved win for the hosts.
Worcester scored three second-half tries through Danny Gray - who also kicked over a conversion and a penalty - David Lemi and James Percival but, after trailing 22-3 at the break, they had little hope of getting anything out of the game. Andy Goode added the extras for the away side.
Irish's win puts them top of Pool Three and they travel to Cardiff for their final game next Friday knowing a bonus-point win would guarantee their berth in the next round.
For Worcester, the defeat virtually extinguishes their hopes of progressing as they are now bottom of Pool Two with five points and stand little chance of overhauling the teams above them.