At the other end, Fernando Muslera did well to bravely block Nani's clipped effort after a smart interchange with Kagawa on the edge of the box.
The Japanese midfielder was involved again on seven minutes for United's opening goal, combining well with Carrick to send the no.16 clear. With Muslera advancing, Carrick shaped to shoot but instead calmly dragged the ball around the goalkeeper.
The stopper's outstretched leg caught Carrick, however, and caused him to stumble. A penalty and a red card loomed, but the Reds midfielder, now on the ground, managed to hook the ball into the empty net with his left foot to open the scoring and spare the Galatasaray goalkeeper further punishment.
The visitors struck the crossbar through Nordin Amrabat soon afterwards but didn't threaten again until Hamit Altintop grazed the base of De Gea's left-hand upright on 38 minutes.
By then, Sir Alex's men had seen two penalty appeals turned down – one for handball by former Arsenal defender Emmanuel Eboue and one for a well-timed tackle by centre-back Dany Nounkeu to halt a tricky Kagawa run – while Valencia's driven delivery from the right almost forced an own goal.
The scoreline at the break will have pleased the Reds boss, but spells of Galatasaray possession and defensive ill-discipline served as reminders that this match was not won yet.
Nani's penalty miss on 53 minutes, after Rafael was brought down by striker Burak Yilmaz, only compounded that feeling. The Reds have now missed three spot-kicks in as many matches – Hernandez and van Persie the other culprits – and must be yearning for the return of Wayne Rooney from injury. This