An early goal from Marc Janko set the Turkish side on course to reach a healthy tally of seven points and Olcan Adin's free-kick defused a late Legia fightback to confirm the win.
News of Lazio's goalless draw at Apollon Limassol then filtered through to the home fans after the final whistle, a result that sees Trabzonspor go two points clear of their Italian rivals in the standings.
Austrian striker Janko has found goals hard to come by since leaving Porto last year but he only needed seven minutes to open the scoring against Legia.
His first close-range effort may have been stopped by Wojciech Skaba but after the rebound came back to his feet in the ensuing scramble, he tucked home.
Chances were at a premium for the rest of the first half but Jakub Kosecki and Tomasz Brzyski both tested home goalkeeper Onur Kivrak.
There was little to cheer after the break either and it was not until the 57th minute that Paulo Henrique forced a brave block from Legia's Jakub Rzezniczak.
Vladimir Dvalishvili sparked the game back into action as time ticked away, his snapshot unsettling Kivrak, whose poor clearance fell to Dominik Furman in a good position.
The Polish midfielder picked his spot from 12 yards but came up against a better save from the recovering Kivrak.
Just when it looked like the visitors might force their way back into the tie, Trabzonspor scored their second goal.
A bad foul on Yusuf Erdogan from Brzyski in the 82nd minute allowed Olcan to step up and steer a free-kick just beyond the reach of Skaba.
Source: Wires
Brazilian forward Claudemir scored a consolation goal in the 88th minute.
The win allowed Galatasaray to climb into second place on four points in the group, five points behind leader Real Madrid. Juventus is third with two points after losing 2-1 to Madrid on Wednesday while Copenhagen is last with one point.
Sneijder had Galatasaray's first attempt in the sixth minute but his effort was saved by Johan Wiland. Three minutes later, however, Brazilian international Melo headed home a ball from Dany Nounkeu to put Galatasaray ahead.
The home team continued pressing, and Sneijder doubled the lead in the 38th after a pass from Emmanuel Eboue.
Eboue also helped fellow Ivory Coast international Drogba to add Galatasaray's third in first-half stoppage time.
The home team, backed by a loud partisan crowd, utterly dominated the Danes in the first half but eased off after the break.
"The match was more or less decided at halftime," Copenhagen defender Lars Jacobsen said. "They scored three fine goals, where they outplayed us completely."
The Danish side seemed more attack-minded in the second half as Galatasaray slowed the pace, allowing Jorgensen and Daniel Braaten to test goalkeeper Fernando Muslera. But Galatasaray continued to press and Wiland made a stunning save in the 61st minute, only to find out that Sneijder had been flagged for offside.
Five minutes later, Drogba found forward Burak Yilmaz whose shot went wide.
Source : AP
But its coach believes it has the will to advance and secure a place for next year's finals.
"Our players are already on their way in their heads and their hearts," he said. "But we also know our tail is still hanging out. The belief is not the same as the reality.
"Obviously the Dutch are not an easy opponent, they are one of the world's best teams.
"They have some of the single most important players in the world. We are aware of this and we intend to do our utmost against them. What we have done in the other games will not be enough, but we are looking forward to it.
"I will not need to give any sort of team-talk. Nothing I could say will add anything extra."
Netherlands has waltzed its way through Group D, amassing 25 points from its seven games, a draw with
Last week's 8-1 thrashing of
But defender
Those fringe players are now getting their chance and are determined to show
Vlaar is among that number, but is determined to prove his worth after starting against Hungary.
"I want to make it as difficult as possible for the coach," he told NUsport. "I had a number of matches under
"But against Hungary I did well I think, as I have always done when I've started. I was able to take more initiative and it went well, although sometimes I need to show more guts."
Match starts at 2:00 New York time ...
