Saints, hot favourites to win League One this season, slumped to their second home defeat in a week after sacking manager Alan Pardew.
Rochdale were content to soak up the pressure and catch Southampton on the break, which they did with great effect.
Southampton had plenty of chances but failed to take any of them and went a goal behind in first-half stoppage time, when Jones led a break from deep inside his own half to set up a simple chance for Chris O’Grady.
Jason Puncheon should have equalised in the 51st minute but somehow managed to shoot over the bar from three yards.
Rochdale got their second in the 68th when O’Grady set up a shooting chance for Jones who beat goalkeeper Kelvin Davis from 25 yards.
Southampton went in desperate search of a consolation with Rickie Lambert, Dan Harding and Joseph Mills all going close but Dale held out for a fine victory.