Craig Bellamy was freed down the left on 22 minutes and transferred the ball to his right foot before curling a cross that drifted over the last defender and went in off Fowler's backside as goalkeeper Faryd Mondragon flapped.
A poor Alonso backpass then gifted Galatasaray striker Necati Ates a clear opening to tuck home the equaliser two minutes later, but there was no-one to blame for the home side moving ahead on 28 minutes when a corner, headed clear by Paletta, dropped to Okan Buruk who unleashed a magnificent 30-yard volley that swerved beyond Dudek.
Fowler had already seen an effort disallowed after Portuguese referee Olegario Benquerenca adjudged Alonso to have taken a free-kick too quickly, while at the other end Umit Karan had beaten Dudek to Sabri Sarioglu's free-kick but headed over.
Liverpool responded to falling behind.
Carragher fired an ambitious effort over then came closer with a header from Pennant's corner that forced Mondragon to save, while the Galatasaray goalkeeper was also equal to Bellamy's shot after the Wales international was played in down the inside right channel by Pennant.
Dudek saved smartly from Sabri, but was rescued by the woodwork nine minutes after the break when Umit Karan glanced a free-kick from Galatasaray captain Ergun Penbe against the post.
Liverpool came close to equalising with a clever set-piece on 58 minutes.
After Junichi Inamoto was booked for encroaching on John Arne Riise's 25-yard blast, Alonso assumed responsibility for the delivery and deceived the home defence by clipping over the wall to Fowler, whose first-time volley was blocked by Mondragon's legs.
Guthrie then shot at the goalkeeper, Riise deflected a Sabri Sarioglu chip wide, Bellamy almost reached Pennant's through ball and Marcelo Carrusca struck an overhead kick at Dudek as the home side slowly started to turn the screw.
And Liverpool's fate was sealed 11 minutes from time when substitute Mehmet Guven left the disappointing Riise on his backside and crossed for fellow sub Sasa Ilic to tap in past an exposed Dudek.
Fowler, though, gave the small band of travelling support some late cheer by heading in at the far post after a fine run and cross by Pennant.
However, it couldn't disguise what had been a revealing night for Benitez.
GALATASARAY: Mondragon, Haspolatli, Tomas, Asik (Seyhan 45), Penbe, Sarioglu, Inamoto, Buruk, Carrusca (Guven 75), Karan, Ates (Ilic 45). Subs: Ercetin, Sas, Topal, Kabze.
BOOKED: Inamoto.
LIVERPOOL: Dudek, Peltier, Carragher, Agger, Riise, Pennant, Alonso (Roque 84), Paletta, Guthrie (Luis Garcia 66), Bellamy (Crouch 74), Fowler. Subs: Martin, Kuyt, Anderson, Darby.
BOOKED: Pennant.
REFEREE: Olegario Benquerenca (Portugal).
ATT: 23,000
NEXT GAME: Liverpool v Fulham, Premiership, Saturday, 3pm
