Liverpool, who would have gone second in the Premiership had they won, piled on the pressure in search of an equaliser but soon found themselves two goals behind.
After 70 minutes, Marian Pahars broke away down the left and his hopeful cross was headed past Jerzy Dudek by Riise, who had only just come on as a substitute for Stephen Wright.
Just a minute before the own goal, Danny Murphy missed Liverpool's best chance of an equaliser.
His smart volley from six yards out was bravely blocked by Saints skipper Jason Dodd.
Liverpool enjoyed slightly the better of an evenly contested first half.
Nicolas Anelka's pace was a constant threat to the Saints defence and he nearly made them pay after just 12 minutes.
The Frenchman beat the offside trap but his poor first touch allowed Paul Williams to intercept and snuff out any danger.
On the half hour mark, Anelka's precise pull back found Jari Litmanen on the edge of the box and his first-time effort was deflected over by the desperate lunge of Dodd.
Litmanen returned the favour on 36 minutes when he set up Anelka for the best chance of the first half.
The Finland international put a neatly controlled header into Anelka's path, as the former Arsenal striker rushed into the box.
As Southampton's defenders struggled to keep up, Anelka fired in a well struck first time shot that was instinctively turned round the post by keeper Paul Jones.
Saints had plenty of possession but their deadly attacking duo of James Beattie and Marian Pahars were well marshalled by the Liverpool defence.
It was substitute Oakley, on in the first half for the injured Rory Delap, who made a real difference to their attack.
His constant runs from midfield troubled the Liverpool back four, resulting in him winning the penalty.
And it was his presence that was troubling Riise when he put through his own net.
Liverpool battled gamely to try to retrieve the situation but the Saints defence stood firm.