Liverpool outplayed and outclassed Brighton for most of the game, but could easily have conceded an equaliser by easing up in the last 20 minutes.
Wing-halves Glen Wilson and Jack Bertolini, after a nightmare first half, suddenly swept back into the game and the Brighton attack at last gave Liverpool backs Molyneux and Moran some anxious moments.
Liverpool played with almost condescending arrogance, especially in the early stages of the second half, and left winger Alan A'Court was superb.
In a badly overworked Brighton defence, Jennings and Little stood up magnificently to the onslaught and Hollins, in goal, had no chances with the goals.
Both sides had chances in the first half before Liverpool went into the lead five minutes before half-time.
Billy Liddell way out on the touch line sent over a long harmless-looking centre, but the Brighton defence was caught napping when Hunt feinting to go through allowed the ball to run to Dave Hickson who crashed it past Hollins.
Unrelenting Liverpool pressure brought the inevitable goal a quarter of an hour after the interval. A glorious pass from Harrower sent A'Court away and Hickson, chesting down the left winger's centre, drove the ball into the net.
Three minutes later, all against the run of play, Brighton reduced the lead when, in their first raid of the second half, Mike Tiddy dropped over a well-placed centre and little Ian McNeill headed a good goal.
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