The crucial match between the two clubs had been postponed from Tuesday, when the game was halted after 31 minutes due to a downpour of hail and snow.
The weather wasn't much better as the game got back under way on Wednesday, as Roberto Mancini's side joined Real Madrid in progressing from Group B amid more snow flurries.
Within seconds of the restart the game looked certain to fall victim to farce yet again when the ball became stuck in the thick brown mud coating the surface, but the flanks were dotted by green patches and play was just about possible over the white dusting in Istanbul.
The best chance of the truncated first half came to Carlos Tevez, who took the ball on following some good hold-up play from Fernando Llorente and burst into the box - but then lost his footing on the slippery turf when swinging his right boot at the ball and only found the side netting.
The viscous surface made a short-passing game near impossible and so it was from a long-ball that Gala claimed the winner on 85 minutes, Didier Drogba flicking it on to Sneijder who took the ball superbly in his stride and stroked a lovely shot into the far corner past Gianluigi Buffon.
The goal meant Gala finished second in Group B while Juventus go into the Europa League - and the Serie A leaders will instantly be among the favourites in a tournament whose final takes place in their home stadium in May.
31’ – MATCH POSTPONED: A storm of nail and snow in Turkey means the match is off! Both teams will return on Wednesday to complete the job. Lucky it’s 0-0….
40’ – CHANCE FOR TEVEZ: Tevez takes the ball into the box and to the right of Muslera following some nice work from Llorente. However, his footing goes as he swings his right boot and the striker finds the side netting.
58’ – BRILLIANT SAVE: Buffon shows a strong arm to repel a vicious effort from Drogba from the edge of the box and Yilmaz swings and misses as the ball rolls free on the rebound.
79’ – JUVE GO CLOSE: Marchisio drills a low shot along the rutted turf after getting the ball from Tevez but Muslera smothers it. Just before that, Gala failed to properly deal with a floated ball into the box from Pogba.
85’ - GOAL! Galatasaray 1-0 Juventus! Wesley Sneijder! Has he put the hosts through? Drogba heads a long pass into the Dutchman's path and he takes the ball in his stride before stroking a shot into the far corner past Buffon.
Galatasaray are unbeaten in their last 10 home games against Italian teams. They have won seven and drawn three of those matches.
Carlos Tevez has now been without a goal in 14 Champions League matches, and 21 games in all UEFA competitions.
Are Galatasaray a team to fear in the last 16? They aren't traditional European powerhouses as such, but Gala have a good manager in Roberto Mancini and two exceptional players in Drogba and Sneijder who showed just how decisive they can be when combining for the winner. Few teams will relish a trip to Turkey in the next round
MAN OF THE MATCH
Wesley Sneijder (Galatasaray): Initially struggled to find his range amid awful conditions at the Turk Telecom arena but gradually settled and then won the game with a quite wonderful goal.
* Note: Ratings decided from 31 minutes onwards.
Galatasaray: Muslera 7, Chedjou 6, Semih 6, Gokhan 6, Eboue 5, Melo 6, Sneijder 7, Selcuk 5, Riera 5, Drogba 7, Burak 5. Subs: Bulut 6, Ceyhun 6.
Juventus: Buffon 6, Barzagli 5, Bonucci 6, Chiellini 6, Lichtsteiner 5, Vidal 6, Pogba 5, Marchisio 5, Asamoah 7, Tevez 6, Llorente 6. Subs: Quagliarella 6, Giovinco 5.
THE MATCH IN A TWEET