Rapid skipper Steffen Hofmann netted the only goal with a second half free-kick to see off a strong Reds side.
Gerrard and Carragher played the first 45 minutes while Benayoun and Holland international Dirk Kuyt came on at the break as Rafael Benitez plenty of changes.
England defender Glen Johnson was not part of the matchday squad, however, after Benitez opted not to risk him after he took a slight knock to his Achilles in Wednesday’s goalless draw against St Gallen.
Rapid had the better of the first half with Erwin Hoffer seeing a goal disallowed for offside while the same player saw a close-range effort well saved by Liverpool goalkeeper Diego Cavalieri.
The goal came after 57 minutes when Hofmann curled a low free-kick past Cavalieri’s replacement Peter Gulacsi.
Stefan Maierhofer had another goal disallowed for offside before, at the other end, Benayoun saw a free-kick well saved by Raimund Hedl.
Benitez introduced Javier Mascherano with 25 minutes to go and the Argentinian’s appearance roused the visitors with Kuyt twice coming close.
Benayoun also came close late on but Liverpool could not find an equaliser.