With the first play of the game, the Reds crafted the kind of move that showed Southampton they were in trouble.
Gerrard found John Arne Riise on the left wing with a pin-point pass and he danced past Paul Telfer before unleashing a cheeky 25-yard effort which produced a fine diving save from Antti Niemi.
Another flurry of creative passes from Gerrard and Alonso moments later left Florent Sinama Pongolle through on goal, but his thunderous shot only met with the sidenetting.
For the Saints, boss Harry Redknapp's announced that his star striker James Beattie had travelled to the game but would not be playing.
He candidly explained that a number of Premiership clubs have expressed interest in the England forward and they were considering offers so that they have some cash to spend in the impending transfer window.
But they were clearly missing Beattie's presence as they struggled to get the ball out of their own half.
It took Southampton more than 35 minutes to produce a shot at goal and even then David Prutton's clumsy effort drifted six feet wide of the mark.
The visitors seemed determined to hold the game up in the midfield and weighed in with several scrappy challenges intended to halt Liverpool's onslaught.
But the Reds appeared to grow a little nervous as their build-up play became stunted and the chances on goal became few and far between.
A trademark sidefooted pass from Gerrard found Sinama Pongolle with his back to goal but he deftly laid the ball back to his captain, who was unlucky to see his effort saved on the line.
It was Sinama Pongolle again moments later who broke the deadlock with a glorious goal from just inside the area.
Midfield maestro Alsonso won the ball on the centre circle and played a perfect pass through two blue shirts for the French striker to run on to.
Without breaking a stride he rocketed a right-foot shot past a helpless Niemi right on the stroke of half-time.
Liverpool's play became complacent, especially at the back which nearly cost them dear when Brett Ormerod found himself with clear shot on goal, but he was too shocked to produce anything remotely threatening.
Salif Diao left the Anfield faithful wondering what he was doing in the squad let alone on the pitch when he gave the ball away three times in the space of two minutes.
His most glaring mistake came when he let the ball bounce right over his head and into the path of the much shorter Kevin Phillips.
The Reds could hardly be pleased with their play against such a poor team, but at least they ground out another win to keep themselves in contention for fourth spot.