Heskey rose to head in a free kick on the right from John Arne Riise for his fourth of the season but there should have been many more in an improved Liverpool performance.
Danny Murphy brought an outstanding save from Antti Niemi after two minutes and the goalkeeper rushed from his line in the 22nd minute to deny Heskey as the big striker raced clear.
Michael Owen shot over the bar when well placed and in the 56th minute should have done better after being put clear by Riise than to shoot across the face of the goal.
Southampton had little to offer in response except hard work and plenty of effort in front of their biggest League crowd ever at St Maryâ€™s.
James Beattie received little service and never looked like adding to his 16-goal tally. The nearest the Saints came to scoring was in the 46th minute when a long shot from Rory Delap was saved at full stretch by the otherwise untroubled Chris Kirkland.
Referee Steve Bennett booked Murphy and Anders Svensson for fouls and frustrated Saints manager Gordon Strachan used three substitutes in a desperate bid to shake off the Liverpool stranglehold but the away side held on for a comfortable win.
Saints boss Strachan said: "Liverpool got a grip early on and we struggled to get going although we had plenty of possession.
"I was disappointed we didn't create more chances and some of our passing was not as crisp or as accurate as it has been in recent weeks.
"But credit to my players because we have gone a long time without losing at home and it is not as though Liverpool outclassed us.â€Liverpool manager Gerard Houllier said: â€œI was so pleased for my players because they worked hard and never gave Southampton any room. We scored only one goal but we had many more chances than they did.â€