Saints defender Jose Fonte was sent off 10 minutes from time before Sunderland substitute Jermain Defoe slid in his 14th goal of the season with six minutes left.
Sunderland, who lost the corresponding fixture 8-0 last season, looked set for a vital win in their battle to avoid relegation before Van Dijk struck with a neat finish three minutes into added time.
Sunderland are one point above the drop zone and Southampton are eighth in the table.
“The dejection amongst us all is clear. It was so important to see this game out. We know how important three points would have been today," Sunderland manager Sam Allardyce told the BBC.
“We dropped a massive clanger in those last few seconds. With the amount of people we had in that box, it’s baffling. We paid a very heavy price."
(Reporting by Ed Osmond; editing by Ken Ferris)
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