The much-maligned England striker's 23rd-minute spot-kick was blocked by Jamie Ashdown, but fortunately for Crouch it did not prove costly as Bolo Zenden was on hand to head home the rebound.
Goals from Liverpool's other out of sorts strikers, Djibril Cisse and Fernando Morientes, wrapped up a comfortable victory and piled the pressure on Pompey boss Alain Perrin.
Portsmouth have not won at Anfield for 54 years and their chances of halting that run looked remote from the first whistle onwards.
After 12 minutes Crouch rose superbly to head goalwards, but the all too familiar sight of the opposition keeper collecting a weak and badly directed effort drew groans from The Kop.
Cisse squandered a good chance before Pompey full-back Andy Griffin gave the penalty away with a crude challenge on Zenden.
Crouch brought more groans from the Anfield faithful, but Zenden spared his blushes.
Morientes replaced the injured Luis Garcia, just in time to see the eager Crouch attempt his version of a bicycle kick after 27 minutes. A Penny Farthing kick might have been a more apt description as Crouch's spindly legs spun through the air but connected weakly.
John Viafara appealed for a penalty after being brought down in a rare foray into the Liverpool box, but, much to the Colombian's disgust, the referee waved play on.
Steven Gerrard and Dietmar Hamann orchestrated play in the middle of the park, but their team-mates still didn't quite look like the unit they undoubtedly have the collective talent to become.
Ashdown made a terrific stop from Morientes 11 minutes before the break to keep Portsmouth in the game, but not for long.
Cisse inadvertently scored a magnificent goal on 39 minutes, as a cross from the right destined for Crouch's head floated over Ashdown and into the top corner of the Pompey net.
Liverpool didn't exactly set the first half on fire with the penalty and a lucky strike, but then again against a poor Pompey, they didn't have to.
The second half began with a more balanced feel as Liverpool looked comfortable at 2-0 and Portsmouth chased the game with renewed vigour.
All the neat passing and movement came from the Reds. Crouch unfortunately looked anything but dangerous as he failed to capitalise on chances in the 52nd and 54th minutes.
Zenden and Gerrard linked well on the wing to push a ball over to Cisse, who almost made it a double fluke, but his floated cross was collected by a more astute Ashdown.
Viafara was yellow carded on 61 minutes for petulantly kicking out at Gerrard after the Reds captain had won the ball from him.
The ineffective Laurent Robert made way for Zvonimir Vukic just after the hour as Portsmouth started to look a little more threatening.
Pompey forced a corner after 68 minutes and Steve Finnan had to be alert to clear Brian Priske's toe poke from the Reds goal-line.
However, no-one could realistically see a Pompey goal on the horizon as the clock ticked down, with both sides seemingly accepting the result.
A Pompey corner saw Sami Hyypia rise majestically to head to Gerrard, who ran the length of the pitch, only to be hacked down.
The free-kick resulted in Morientes' 80th-minute goal. The ball was played into the box and the Spaniard exchanged passes with Hyypia before turning it home from close range to put the home side 3-0 in front.
Pompey chairman Milan Mandaric must now be close to making his threat to dismiss Perrin a reality after this impotent display.