Buoyed by Reading's defeat at Arsenal in the early kick-off, Fulham set about their task with renewed vigour and caused Liverpool's central defensive pairing of Sami Hyypia and Martin Skrtel several anxious moments.
But, as has so often happened this season, Fulham's early promise gave way to slapdash defending which Liverpool punished in the 17th minute.
Moments after Peter Crouch had flashed a header just wide, a quick exchange of passes in midfield between Javier Mascherano and Lucas Leiva allowed Pennant to accelerate past Brede Hangeland and fire a right-footed shot past Kasey Keller from a tight angle.
Pennant was close to setting up Crouch moments later, but his low cross was just too far in front of the rangy striker and Paul Stalteri cleared John Arne Riise's follow-up from under his own crossbar.
Against the run of play, Fulham came close to forcing an equaliser five minutes before half-time but Hangeland failed to react quickly enough when David Healy's cross deflected into his path and the Norwegian defender sent his header a yard wide.
Jamie Carragher replaced Hyypia at the start of the second half but the change did nothing to alter Liverpool's supremacy.
Indeed, Benitez's side had chances to kill off Fulham's survival hopes only for Andriy Voronin's bicycle kick to clear the crossbar by a matter of inches, and Yossi Benayoun showed why he is without a goal since January with two powder-puff attempts from close range.
But 20 minutes from time Crouch put the game beyond the reach of the Reds' struggling hosts when the England international gleefully collected Pennant's pass and fired a low shot through Keller's legs.
Danny Murphy had the chance to pull a goal back five minutes later when he was played in by Healy, but Pepe Reina's leg proved the latest in a long line of insurmountable obstacles that Fulham have failed to clear this season.