The score could have been more, though, as Hull seemed to capitulate after the loss of key defender Michael Turner at half-time.
In an open first period it was Hull who wasted two golden opportunities to take the lead. First, experienced Dean Windass headed embarrassingly wide from a Sam Ricketts cross with the goal at his mercy and then defender Damien Delaney could only direct Jay-Jay Okocha's long ball over the bar.
They were made to pay by a Southampton side who before the game had just one home goal in their last four appearances at St Mary's.
Wright-Phillips used all his neck muscles to stretch at the far post and connect with the impressive Adam Hammill's cross to give the home side the lead going in at the break.
Turner was replaced and from that point on Hull never looked the same side that had enjoyed much of the first-half play.
John grabbed his first of the afternoon after more good work from Hammill as the on-loan Liverpool midfielder cut back on to his left foot and clipped the ball in for the Trinidad & Tobago striker to finish past by Boaz Myhill.
On-song Hammill was causing Hull increasing amounts of problems and it was another of his runs which brought about a third goal, as he tore down the right before his cross found its way to John who finished with the aid of a deflection.
The former Coventry and Birmingham striker then sealed a match-winning performance with a sublime third, as he beat Myhill from 25 yards with a scintillating left-foot volley.