Bath Rugby took less than 60 seconds to kick-start their campaign against Bucharest Wolves, whilst Agen won on the road against a tough Calvisano side.
Bath's Sam Vesty scored a penalty before repeating the process 10 minutes later to race to a 6-0 lead within 11 minutes.
Bath forwards Will Spencer and Ross Batty both crossed the white line in the first half as Sam Vesty proved his worth, kicking 15 points and securing himself a 45th minute try.
The 2008 tournament champions never looked like losing as they raced away in the second half to secure a bonus point and place them at the top of the table. Travelling to Agen in Round 2 will prove a different challenge, but for now Bath can move forward with a certain degree of confidence.
Having not reached the knock-out stages of the competition since 2005, Agen paved the way for all that to change with a narrow five-point victory over Calvisano at the Peroni Stadium. The two teams exchanged early tries before Agen turned up the pressure with a further three first-half tries against Calvisano's two.
The Agen dominance of the first half was nearly undone as the Italian hosts staged a remarkable late comeback to close the gap to a mere five points at the final whistle, securing an invaluable two bonus points along the way.