The thrilling game marked the beginning of a record 18th campaign in the competition for the Red Devils as Sir Alex Ferguson’s side were given a testing time by the Turkish Süper Lig leaders.
“To pick up three points in the opening match is very important, especially when you look at what happened last season,” said Ferguson.
“In the first half we gave the ball away too often and they counter-attacked really well. In the second half, though, we were much more solid at the back, and all the chances fell to us.
“It was a good game, they were very confident in possession, and we kept ourselves on edge in the second half after missing chances in the second half.”
There was a scare for the hosts after just 33 seconds as Umut Bulut appeared to be fouled in the penalty area by Nemanja Vidic, but referee Wolfgang Stark was unmoved.
After an even start, Galatasaray’s goal came under threat in the sixth minute, but Fernando Muslera did well to keep out Nani’s attempted chip.
The visiting defence was breached again moments later as the deadlock was broken.
After exchanging passes with Shinji Kagawa, Carrick ran into the box and neatly tucked the ball into an empty net, despite Muslera’s attempts to stop him.
Statistics suggested that this goal would lead to a home victory, with just one of 60 home Champions League games being lost after they opened the scoring.
Despite going behind, Fatih Terim’s side were not out of the contest, with Nordin Amrabat’s 20-yard curler striking the top of the crossbar.
But the Turkish side did not appear to be fazed by the setback and they hit the woodwork for a second time in the 38th minute, as Hamit Altintop went close.
United were presented with a golden opportunity to extend their lead eight minutes into the second half, as Rafael was brought down in the box by Burak Yilmaz’s clumsy challenge.
But Uruguayan goalkeeper Muslera came to the rescue of his side as he pulled off a great save to keep out Nani’s stuttering spot-kick attempt.
Incredibly, that third penalty failure of the season meant that Sir Alex’s side have already missed as many spot-kicks as they did in the whole of 2011-12 campaign.
Soon after, the hosts were nearly punished for their wastefulness as Altintop’s teasing cross was met by Inan, who glanced his header onto the far post of David De Gea’s goal.
The match became an open affair with chances at both ends in the final 20 minutes.
First, Patrice Evra was kept out by Muslera, before De Gea made a double save to deny the counter-attacking Aslan.
Substitute Javier Hernández wasted a trio of chances to make the game safe late on but United managed to preserve their solitary advantage and pick up the three points.