Substitute Odsonne Edouard's fantastic finish gave 10-man Celtic a dramatic 3-2 win over Rangers in a classic Old Firm match at Ibrox.
Rodgers has not lost in eight matches against Rangers since he took over at Parkhead in 2016 and has won three out of three at Ibrox.
Celtic manager Brendan Rodgers dismissed links to replacing Arsene Wenger at Arsenal, insisting that he is happy to be coaching in Scotland.
Rangers produced another ruthless display as they smashed St Johnstone 4-1 at McDiarmid Park.
Celtic moved back nine points clear of Rangers at the top of the Scottish Premiership with a 10th successive win over Aberdeen.
Rangers closed to within six points of Premiership leaders Celtic with an impressive 2-0 win over Hearts at Ibrox.
A much-changed Celtic side failed to hit their European heights as St Johnstone held them to a goalless Scottish Premiership draw at Parkhead.
Josh Windass scored a hat trick as Rangers moved back up to second in the Scottish Premiership following a 5-3 comeback victory over Hamilton.