The win moves Celtic level with Bayern Munich in Group B, and establishes a crucial advantage over Anderlecht.
Griffiths’ opener was created by a fine passing move involving Olivier Ntcham and Kieran Tierney.
Kara Mbodji inadvertently deflected Roberts’ shot in after the break then Sinclair crashed in a late third.
Celtic: Rodgers delighted with ‘outstanding performance’ in Brussels
The only setback for Celtic was the departure of captain Scott Brown during the second half, the midfielder limping off with what appeared to be a hamstring injury.
He could now be a doubt for Scotland’s World Cup qualifying double header against Slovakia and Slovenia, but for Celtic this was their first away shut-out in the Champions League group stage.
Celtic began nervously, and for the opening 25 minutes they couldn’t hold on to the ball, their passing letting them down hugely. From Ntcham to Roberts, they coughed up possession constantly and invited Anderlecht on to them.
Celtic striker Leigh Griffiths
Celtic striker Leigh Griffiths finished emphatically after a fine passing move involving Olivier Ntcham and Kieran Tierney
The saving grace was that the Belgian side, beleaguered in their domestic league, were nowhere near good enough to take advantage.
Celtic settled when the goal came – and it was a beauty, a study in accurate and clinical football, the polar opposite of what had gone before.
It began with Ntcham, who delivered a gorgeously weighted pass to Tierney, scampering down the left flank. The timing of the pass and the run were exquisite, as was Tierney’s driven cross to Griffiths, who had cleverly peeled away from Olivier Deschacht in the box.
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