Galatasaray, Juve fight for points share
Substitute Fabio Quagliarella thought he had won it for Juventus with an 87th minute header but Umut Bulut immediately equalized.
A howler from Juve defender Leonardo Bonucci had gifted Didier Drogba the opener for Galatasaray in the 36th minute before Arturo Vidal levelled from the penalty spot after Quagliarella was harshly adjudged to have been fouled by Nordin Amrabat.
Former Inter Milan and Manchester City coach Mancini was confirmed as Fatih Terim's replacement on Monday and only met his new players for the first time shortly before their flight to Italy.
Real Madrid, which beat Galatasaray 6-1 in their opening match, won 4-0 at home to FC Cophenhagen to take firm control of Group B.
Both sides had endured a disappointing start to their European campaigns and they started cautiously in Turin. Juventus had the first real opportunity in the 15th minute, but Paul Pogba slipped as he attempted an audacious overhead kick and missed the ball completely.
That seemed to spark the game into life and Drogba almost put Galatasaray in front four minutes later with a shot from a tight angle which Juventus goalkeeper Gianluigi Buffon did well to clear with his foot.
A setback followed shortly afterward for Juventus when Mirko Vucinic beat the offside trap to race onto a delightful chipped pass by Andrea Pirlo, but stumbled and injured himself in the process.
Vucinic receieved treatment on the pitch but was replaced minutes later by Quagliarella, while Galatasaray defender Semih Kaya made way for Gokhan Zan.
Quagliarella almost gave Juventus the lead with his first touch in the 28th minute as he prodded a cross narrowly past the left post. The Juventus forward was caught up in a tangle with Zan as he struck the ball but the referee waved away his furious claims for a penalty.
Galatasaray broke the deadlock when Bonucci woefully misplaced a back pass, giving it straight to Drogba, who easily bypassed the outrushing Buffon to slot into an empty net.
Juventus almost leveled shortly afterwards but Carlos Tevez's fierce shot scraped the outside of the right post moments later.
Galatasaray could have extended its lead when Wesley Sneijder was left completely unmarked and blazed well over the crossbar from just inside the area.
Juventus defender Stephan Lichtsteiner also picked up an injury and was replaced by Mauricio Isla for the start of the second half.
The hosts immediately upped the pressure in the second half and Kwadwo Asamoah curled a shot just past the top right corner from the edge of the area.
Arturo Vidal also went close as he twice fired narrowly over the crossbar in quick succession.