The Socceroos midfielder slotted through Patrick Roberts with a well-timed assist in the 34th minute, 12 minutes before he clashed heads with Juwon Oshaniwa, who was later sent off for a second bookable offence.
The fixture lined itself up as a potential stumbling block for Ronny Delia’s side with the third-placed visitors boasting four wins from their past five games and just as many clean sheets.
However, after Celtic’s Jamie Walker had his opener cancelled out by Gary Mackay-Steven, 19 year-old Patrick Roberts came to the rescue with two fine strikes in each half as the Hoops remain seven points clear at the top of the Scottish Premiership.
Rogic looked lively in the opening half and his willingness to win the ball back paid off when he made a fine interception on the right hand side before striding forward and knocking the ball through to Roberts, who delicately lobbed the ball over Alexander.
Delia hopes Rogic will return to action shortly and believes the substitution was a precautionary measure.