The Belgians have been in a bit of turmoil recently and have recently sacked their manager, however the Bhoys' less than stellar away record on their travels in Europe meant that a positive result was by no means a foregone conclusion.
After a nervous opening half hour Griffiths broke his duck in the group stages proper, firing home a Kieran Tierney cross.
"It was great, we had a huge result at the weekend and it was good to bounce back and do it again in the Champions League".
The national team captain was replaced by Nir Bitton in the 70th minute at the Constant Vanden Stock stadium with the Scottish champions leading through a Leigh Griffiths goal and a deflected strike by Patrick Roberts.
Brendan Rodgers believes the roots of Celtic's long-awaited away win in the Champions League were planted a year ago.
It was Rodgers' first Champions League win as Celtic boss - the Hoops drew three games last season - and he believes they can get even better. I think we came out with flying colours.
Let no-one question the brutality of the Champions League.
There was a significance to Celtic's 3-0 win at Anderlecht on Wednesday evening that moved beyond the reinvigoration of a Champions League campaign.
"We did very, very well".
Scott Sinclair added shine to the scoreline in stoppage-time, but Rodgers will not underestimate the huge task that still faces his side in attempting to qualify from a group that also includes Paris Saint-Germain and Bayern Munich.
"You saw the concentration of the players - how many times Anderlecht were caught offside, our defensive line was very good". I think Lenny was the last in 2012 and before that God knows when a Scottish team has won away from home.