Ahead of the match, Celtic, Scottish champions for the past six seasons, had only won once in 30 away matches in the Champions League.
Having been thumped 5-0 at home by Paris Saint Germain in their opening match, Celtic are third behind Bayern Munich on goal difference after the German side's 3-0 loss to Paris St Germain.
After 37 minutes in which neither team managed a single shot on goal, Celtic flawlessly executed a counter from their own half to gain the lead, with Leigh Griffiths converting calmly.
Five minutes into the second half, Celtic scored again when a cross by Patrick Roberts came off Anderlecht defender Kara Mbodji into the net, before Scott Sinclair made it 3-0 with a thumping shot in the final seconds.
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Anderlecht, who sacked manager Rene Weiler this month after a disappointing run in the Belgian league, are last in the group, having also lost their opening match against Bayern.
(Reporting by Robert-Jan Bartunek; Editing by Rex Gowar)
