Beattie opened the scoring six minutes into the second half with his 13th goal of the campaign after being set up by Phillips as Southampton broke from a Liverpool corner.
Phillips wrapped up the three points for the home team when his 25-yard right-foot strike five minutes from time was deflected over Liverpool goalkeeper Jerzy Dudek into the bottom left-hand corner of the net.
But the real hero was Saints keeper Antti Niemi who produced a series of brilliant saves to deny the visitors and place Liverpool boss Gerard Houllier's job under increasing pressure.
Niemi presented a one-man barrier to Liverpool at times and capped his great display by moving smartly to his right to keep out a 72nd minute penalty from Michael Owen.
Liverpool were forced into a late change to their starting line-up prior to kick-off when Bruno Cheyrou damaged an angle in the warm-up and Harry Kewell was promoted from the subs bench.
It was Kewell who forced the first save out of Niemi in the ninth minute when the Finnish keeper tipped his goalbound shot from the edge of the area wide.
Niemi also did well to block efforts from Igor Biscan and Owen before the half-time break while Southampton failed to muster a single shot on target.
However, the home side took the lead against the run of play in the 51st minute when Phillips fed Beattie who comfortably finished past Dudek and the goal prompted Liverpool to surge forward in growing numbers.
Niemi then denied Biscan again while the Saints keeper produced a wonder save on 58 minutes to keep out Steven Gerrard's eight-yard effort and Owen's follow up hit the post.
Owen had the perfect chance to equalise 18 minutes from the final whistle after Jason Dodd was adjudged to have tripped Kewell but Niemi was in unstoppable form guessing right to keep out the England striker's effort.
Owen was made to pay the price for his miss as Phillips shot home from long range in the 85th minute to complete a memorable victory for Sturrock.