Liverpool comfortably beat Portsmouth, though Peter Crouch's goalscoring drought shows no sign of ending.
Crouch's first-half penalty was saved by Jamie Ashdown, but Boudewijn Zenden spared the Liverpool striker's blushes by heading in the rebound.
Pompey's best player Ashdown enjoyed little luck, the Portsmouth keeper conceding a second goal when Djibril Cisse's cross floated into the net.
On 80 minutes Fernando Morientes added a third, cleverly hooking the ball in.
Brian Priske had Pompey's best chance when he missed from close range midway through the second half.
Following a corner the Dane arrived emerged from a pack of players he was unable to get any power on his shot and Jose Reina spooned the ball away.
Even given the luck Liverpool enjoyed for their first two goals, Rafael Benitez's side were well worth the win, their third successive league victory.
Portsmouth's strategy was to contain Liverpool and to try and use Lomano LuaLua's speed on the counterattack.
It was a strategy that unravelled as Liverpool overran the visitors, who were frequently outmuscled.
Crouch must be wondering just what he has to do to break his Liverpool duck in what was his 16th game since moving to Anfield.
Although he continues to lead the line with confidence, his finishing remains anxious and at times clumsy.
Before his penalty miss against one of his old clubs Crouch had been denied by Ashdown's reaction save as the Portsmouth keeper did well to push the Liverpool striker's header away with one hand.
The award of the penalty by referee Peter Walton was a little fortuitous given Zenden's rather dramatic fall following Andy Griffin's slight push on the Dutchman.
Crouch's poorly taken spotkick was saved by Ashdown but Zenden headed in the rebound despite Gregory Vignal's efforts to hook the ball away.
Early in the second half Crouch broke clear and blasted a shot goalward that Ashdown beat away.
It was primarily due to Ashdown's heroics that the scoreline had a degree of respectability as Portsmouth struggled to break out of their own half.
The Portsmouth keeper superbly palmed away Morientes' header and soon after Ashdown rushed out to gather the ball when the Spaniard threatened again.
Morientes had come on for the injured Luis Garcia's after Liverpool's first goal, a substitution that saw Cisse deployed on the right wing.
Six minutes before the interval Cisse scuttled down the right and lofted a cross towards the far post.
Much to the Frenchman's bemusement the ball sailed over Ashdown's head to land in the net.
Liverpool's third goal was due to poor defending rather than luck, the Pompey defence labouring to clear a Steven Gerrard cross, allowing Morientes time to clip the ball past Ashdown.
Liverpool manager Rafael Benitez:
"Peter Crouch played really well and was unlucky because the keeper made some good saves.
"Peter is one of our chosen penalty takers and it was his decision to take the kick because he felt confident.
"We played well - we scored goals and had many chances."
Portsmouth manager Alain Perrin:
"I've no thought of my own position, I'm only concerned about how we play in the hope that we can get points to get away from the bottom.
"Their first was a fortunate penalty and the second was lucky because I don't think Djibril Cisse meant it.
"We did not play well in the first half but we were better in the second half."
Liverpool: Reina, Finnan, Carragher, Hyypia, Warnock, Gerrard (Josemi 83), Hamann, Zenden, Luis Garcia (Morientes 22), Crouch, Cisse (Alonso 69).
Subs Not Used: Dudek, Traore.
Goals: Zenden 23, Cisse 39, Morientes 80.
Portsmouth: Ashdown, Griffin, O'Brien, Priske, Vignal, Viafara, Hughes (Skopelitis 74), Taylor, Robert (Vukic 64), O'Neil, LuaLua (Mbesuma 70).
Subs Not Used: Westerveld, Primus.
Ref: P Walton (Northamptonshire).