It had all looked to be so easy when Stelios fired the home side into a 26th minute lead, but after missing a hatful of chances, they were made to pay when Kevin Phillips grabbed a second-half equalizer for the Saints.
Both sides had chances to win it in the end, but had to settle for a result that did little to help their respective causes at the top and bottom of the table.
After losing a 2-0 lead against Villa on Saturday, Southampton's cautious start was hardly surprising but in the early stages they dealt comfortably with all Wanderers had to offer.
Antti Niemi foiled Kevin Nolan and Stelios as they scrambled for the ball in the Southampton goalmouth, before an on-target Fernando Hierro shot was deflected wide.
Yet Southampton's composure was finally broken in the 26th minute when El-Hadji Diouf bamboozled Graeme Le Saux on the by-line, and crossed to the far post where Stelios powered in a close-range header.
Suddenly Saints fell apart, leaving Wanderers to produce a full range of tricks that should have given them a comfortable lead.
Diouf let fly with a shot that stung Niemi's hands and then the Finnish keeper was almost caught out by a 40-yard Jay-Jay Okocha snapshot.
Another goal should have followed immediately after half-time as the keeper beat out Gary Speed's header and Diouf somehow put the rebound over the bar from six yards.
Yet Wanderers were given a wake-up call in the 55th minute when Saints suddenly carved out three openings. Peter Crouch had a header blocked before Jussi Jaaskelainen saved from Matt Oakley, who then fired the rebound high over the bar.
But it was enough to give the relegation-threatened visitors the confidence to go forward and when Rory Delap fired a long ball into the area in the 69th minute, Phillips seized on the chance to slip the ball past Jaaskelainen for a 69th minute equaliser.
Wanderers should have been back in front when substitute Kevin Davies crashed the ball against a post before Okocha fired another chance narrowly wide.
Yet Southampton were not taking things lying down and they could have gone ahead in the 80th minute only for Phillips to fire over from Crouch's knockdown.
Wanderers should have had the points wrapped up in the closing minutes when Stelios and Davies both missed from close range.