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Tessem’s close-range header appeared to be blocked on the line by a Sunderland defender before being bundled into the net.
Only after four replays on the giant screens at Saint MaryÂs did it become clear that the header had gone over the line.
Saints manager Gordon Strachan said: “I am delighted for Jo. He did brilliantly at Chelsea on Boxing Day and played well when he came on.
“He picked a perfect moment to score his first goal of the season.”
All of which was hard luck on Sunderland who had defended dourly and had held on under increasing pressure.
Austrian goalkeeper Jurgen Macho had kept Sunderland in the match with outstanding saves in the first half from Paul Telfer and Fabrice Fernandes and in the second period from Chris Marsden.
But it was Sunderland who went closest to scoring 30 seconds after the break when Michael Proctor, who had just come on as a substitute, hit the outside of the post.
Southampton went ahead in the 73rd minute when James Beattie headed in a centre from Marsden for his 12th of the season.
But Sunderland fought back to equalise four minutes later when Gavin McCann took a corner on the right and another substitute, the lanky Tore Andre Flo, rose above the defence to head in.
Beattie missed a clear opening in the 79th minute and just as the game appeared to be heading for a draw, Tessem came up with his winner to preserve Saints’ unbeaten home record.