The Socceroos star delivered a workman like 90 minute shift for the Hoops in the win to move into second spot in Group B.
Scottish left back Kieran Tierney opened the scoring for Celtic after only 11 minutes with a laser like driven shot from just inside the 18-yard box to give the home side a 1-0 lead.
When Jean-Kevin Augustin equalised 78 minutes in, RB Leipzig thought they had done enough to snatch a point.
However, Celtic weren't going to lie down and hit back less than 60 seconds later through Odsonne Eduoard who fired home the winner from close range.
Leipzig pushed hard in the dying stages but it wasn't to be as Celtic claimed the 2-1 win which moves them to six points and level with their German opponents in second spot in Group B after four matches.
Rogic missed Celtic's last two Europa League matches and his return to the line-up for this match helped steel Brendan Rodgers side against a resurgent Leipzig outfit.
Playing in his preferred attacking midfield role, the Canberra native had the opposition defence on their toes with his slick dribbling and pinpoint passing.
Although not getting on the scoresheet, Rogic's movement and passing helped in the early buildup play of Eduouard's match winner.
Celtic's next Europa League clash is at home against the Rosenborg side of fringe Socceroos defender Alex Gersbach on November 30.
In Belgium, Danny Vukovic's Genk side snatched a 1-1 draw against Turkish side Besiktas in their Group I clash at the Cristal Arean.
It was a mixed performance for the former Sydney FC shot stopper in a match when he was rarely tested.
Vukovic was unable to stop cult Portuguese winger Quaresma from opening the scoring for Besiktas in the 16th minute despite getting a glove to the ball after rushing up to stop a breakaway.
Despite struggling to threaten in attack, Genk found an equaliser in dramatic fashion as a long range effort from substitute Sander Berge found the back of the net after taking a deflection.
Genk remain on top of their Group after four games on seven points with two wins and and a draw.
Vukovic's next Europa League clash with Genk is on November 30 when they travel to Sweden to take on Malmo.
It was a tough night at the office for Alex Gersbach as his Rosenborg side was thrashed 5-2 by Red Bull Salzburg.
The Aussie defender was forced to watch on from the bench as his side struggled to stop a relentless Salzburg outfit.
Japenese striker Takumi MInamio was the star for Red Bull claiming a hat trick in the win.
Minamino opened the scoring after six minutes with a composed finish before claiming his brace 19 minutes in when he found the back of the net with a cool half volley.
He wrapped up his hat trick on the cusp of the interval of half time.
Rosenborg showed signs of life in the second stanza with two goals but it was too little too late with their Austrian opponents scoring again to wrap up the comprehensive win.
The result leaves Rosenborg pinned to the bottom of group B with their next match against Tom Rogic's Celtic on November 30.
Finally, fringe Socceroos striker Apostolos Giannou played 90 minutes for Cypriot club side AEK Larnacca as they played out a scoreless draw with Bulgarian side Ludogrets.
The match was largely bogged down in midfield with Giannou managing only two shots on goal.
The result leaves AEK Larnacca at the bottom of Europa League Group A tied with Ludogrets on two points after four matches.
Their next match is a clash against Group A leaders FC Zurich on November 30.
