Kuyt then couldn't quite connect with Aurelio's low cross from the left, Garcia slashed a shot off target following the Dutchman's lay-off and Mondragon was almost deceived by a swerving Gerrard piledriver, the goalkeeper eventually clearing with his legs after ending up diving the wrong way.
And the goalkeeper then had to be alert to rush outside his area and clear from Kuyt following former Liverpool defender Rigobert Song's poor header.
But Galatasaray finished the half the stronger as they gradually began to exploit the gaps down Liverpool's flanks.
Sabri Sarioglu shot wide and saw a dangerous cross palmed away by Pepe Reina, who was also equal to Cihan Haspolatli's angled drive after Sasa Ilic's pass had sent the Galatasaray right-back clear in behind a dozing Garcia.
However, it was Liverpool who struck again seven minutes after the interval with Crouch's moment to remember.
After Ayhan Akman had lost the ball, Finnan sped beyond Orhan Ak and delivered a cross from the right flank that Crouch met with an acrobatic overhead kick that flew in past a sprawling Mondragon.
It was from a position similar to the one which Crouch had spurned a similar chance for England against Trinidad and Tobago in the World Cup.
The subsequent photo became something of an internet phenomenon, but the striker had the last laugh.
Both sides then hit the woodwork, Sabril Sarioglu striking the base of Reina's right-hand post with a curling free-kick while Kuyt rattled the frame of the goal with Gerrard's follow-up striking the prone Mondragon on the leg.
But, reinvigorated by a pair of attacking half-time changes by coach Eric Gerets and with Liverpool momentarily relaxing, Galatasaray dragged themselves back into the game with two headed goals in six minutes from substitute Umit Karan.
The first came on 59 minutes when Arda Turan kept the ball in down the left and delivered a cross for the forward to score. Then, from the other flank, Ilic played the ball in and Karan was left unmarked to nod home his second.
Gerrard almost calmed the frayed Anfield nerves with a shot that fizzed wide from the edge of the area and, for all their possession, Galatasaray actually threatened more than they delivered.
However, after Ilic screwed one effort woefully wide, Hakan Sukur nodded a decent opening right at a grateful Reina and then completely missed his kick in the final minute of injury time.
Liverpool, though, held on. Benitez's new-look team may be easier on the eye but not so on the nerves.
LIVERPOOL (4-4-2): Reina, Finnan, Carragher, Agger, Aurelio, Pennant (Sissoko 78), Alonso, Gerrard, Luis Garcia, Kuyt (Gonzalez 66), Crouch (Bellamy 90). Subs: Dudek, Hyypia, Riise, Zenden.
BOOKINGS: Alonso, Finnan.
GALATASARAY (4-4-2): Mondragon, Haspolatli (Karan 45), Tomas, Song, Ak, Sari-oglu, Topal (Sas 45), Akman, Turan (Carrusca 86), Ilic, Sukur. Subs: Elmas, Buruk, Asik, Kabze.
BOOKINGS: Akman, Sas.
REFEREE: Luis Medina Cantalejo (Spain)
ATT: 41,976.
NEXT GAME: Bolton v Liverpool, Premiership, Saturday, September 30, KO 12.45pm
