Phillips, who this week described last year as the worst of his career, should have settled the match in the 58th minute after David Prutton had got clear down the right.
Prutton's low centre found Phillips clear in the six-yard box, but he could only scuff his shot wide when it looked easier to score.
The miss summed up the match as a spectacle and in the end both sides would have been satisfied to have earned a point.
Leicester were at their attacking best in the first half and Muzzy Izzet saw a free-kick from 20 yards, assisted by the wind, punched from the line in unorthodox fashion by Antti Niemi.
Veteran striker Les Ferdinand should have done better in the 24th minute than to guide a left-foot shot wide from 15 yards, but it was Southampton who had the majority of the possession.
French winger Fabrice Fernandes, recalled after five matches, shot across the face of the goal after being set up by James Beattie and leading scorer Beattie also wasted a clear opening to add to his 11 goals.
Southampton were not helped when they lost influential defender Claus Lundekvam with a hamstring injury before half time and Leicester almost snatched a surprise winner with three minutes remaining.
Paul Dickov, who had replaced the tiring Ferdinand, shot inches wide from almost 30 yards, after finding room while the Southampton defence retreated.
Izzet ruined a good evening's worked by being booked and there were yellow cards also for Southampton defenders Danny Higginbotham and Michael Svensson.
Southampton: Niemi, Dodd, Michael Svensson, Lundekvam (Delap 42), Higginbotham, Telfer, Anders Svensson, Prutton, Fernandes (McCann 77), Phillips (Delgado 83), Beattie. Subs Not Used: Jones, Ormerod. Booked: Higginbotham, Michael Svensson.
Leicester: Walker, Impey, Dabizas, Howey, Stewart, Thatcher, Izzet, Scowcroft, Davidson, Bent, Ferdinand (Dickov 64). Subs Not Used: Coyne, Heath, Hignett, McKinlay. Booked: Izzet.
Referee: H Webb (S Yorkshire).