The Fulham striker has been linked with a £7 million move to Manchester United but after this performance a much higher fee would be needed to tempt Chris Coleman to sell his biggest asset.
Saha was in devastating form as he took his tally for the season to 12 with strikes either side of half-time.
But Southampton can have little to moan about after Gordon Strachan's men turned in a dire festive performance.
Saha went close for the home side early on with a deflected drive and Martin Djetou should have done better with a header on six minutes but nodded the wrong side of Antti Niemi's post.
James Beattie tried to rally his team-mates with some fierce runs, but it was Fulham who took the lead through Saha.
A neat one-two between Lee Clark and Steed Malbranque ended with the latter finding Saha, and the French striker made no mistake as he coolly tucked the ball across Niemi and into the far corner.
Luis Boa Morte had a chance to increase Fulham's lead after 21 minutes but after taking too long to fire a shot away he tried to tee up Saha - only this time he was unable to find a finishing touch.
Southampton twice came close through long-range Paul Telfer efforts but not before Clark had fired a drive towards the top corner which Niemi did brilliantly to keep out.
Fulham stepped up the pressure in the second half and Moritz Volz signalled what was to follow as he skinned Neil McCann before finding Saha, who shot wide.
Saints keeper Niemi was undoubtedly the visitors' best player and it was just as well he was on top form, as his goal continued to be bombarded by Fulham efforts.
The Finnish international saved brilliantly from Saha just before the hour mark and substitute Kevin Phillips then came closest to a leveller as his long-range shot was tipped wide by Edwin Van der Sar.
But if Saints thought that was a sign of a change in the game they were wrong as Boa Morte used his pace to knock the ball past Chris Marsden on 61 minutes and the midfielder lunged in with a late tackle to chop down the Portuguese international.
Referee Dermot Gallagher pointed to the spot and top scorer Saha wasted no time in putting the ball down and placing a side footed penalty straight down the middle.
Niemi was on top form again as he somehow managed to palm away two magnificent Boa Morte drives, but Malbranque will be disappointed that he did not get his name on the score sheet as he hooked the ball over the bar from two yards on 70 minutes.
Gordon Strachan threw on striker Agustin Delgado in a bid to rescue a point but the closest he came to finding the back of the net was when Zat Knight bundled him into the post.
Clark came close with a late effort but Saints wasted no time in leaving the pitch after a disastrous day in London.