The Lotto Belisol rider had a problem with his chain which prevented him from getting involved in the sprint to the line on the second stage, but bounced back in style as he blasted his way to another superb sprint victory - and with it the lead in the general classification.
Peter Sagan came second and Nacer Bouhanni third, with a host of other stars - including Team Sky's Chris Froome and Leopard Trek's Fabian Cancellara - dropping off the pace in the closing stretch at the end of the 145km stage.
The 10 bonus seconds for winning the stage see Greipel dislodge Leigh Howard at the top of the standings, though he is likely to lose it on Friday as the riders face four steep laps of a loop to the top of Bousher Almarat at the end of the 173km fourth stage.
Stage three result
1. André Greipel (Germany) Lotto-Belisol
2. Peter Sagan (Slovakia) Cannondale
3. Nacer Bouhanni (France) FDJ.fr