An Olivier Ntcham goal sealed Old Firm victory for Celtic and consigned Steven Gerrard to his first defeat as manager of Rangers.
Rangers defended manfully but were undone just after the hour when Olivier Ntcham finished off a stunning counter attack for Brendan Rodgers' side.
Celtic struck the woodwork four times as Rodgers' extended his unbeaten Old Firm run to 12 games.
The result means Rangers have now not won a league derby since March 2012.
And it leaves the Ibrox side seventh in the Scottish Premiership with just one win in four games, while Celtic move up to second - three points behind leaders Hearts.
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Steven Gerrard