The Lotto-Belisol rider, who claimed three stages on the Tour of Belgium last week, held the front after a breakaway by Jens Voigt (RadioShack Nissan) was caught 11km from the finish.
Davide Appollonio (Sky) was second ahead of Samuel Dumoulin (Cofidis) and Romain Feillu (Vacansoleil).
Jesus Rosendo Prado made the first break from the start, but Albert Timmer (Argos-Shimano) caught him to win all three mountain sprints.
"I waited but nothing happened,” he said of the lack of a counter-attack. “Then I went after him because I wanted to go for the mountain jersey.
"The only way to defend it is to be in the breakaway again, so we'll see tomorrow."
The duo was caught in Hesperange ahead of the circuits there. Voigt then attacked, building a lead of three minutes on the peloton and 1:15 on Martin Mortensen before the latter pulled back as a result of the wind.
"I really believed I had a chance," Voigt said. "If they started too late with the chase I could have won the stage and yellow. Now I will work for the team and maybe I'll get another chance to attack."
Greipel said: “We were quite afraid of Jens because he is such a strong rider. The team's goal was to win a stage and I did that. We'll see what tomorrow brings.”
Jimmy Engoulvent, who won the prologue, kept the yellow jersey.
The second stage is a 183.9km run from Schifflange to Leudelange.