Saints, who would have gone level with Middlesbrough in the final play-off place with victory, thought they had held on for a draw when Jack Rose saved Joe Grayson's 84th-minute penalty.
But Southampton goalkeeper Rose was beaten when Evans curled in the decisive goal from the edge of the penalty area.
Blackburn will guarantee the Division 2 title and automatic promotion to Division 1 with three wins from their last four matches. They are four points clear of nearest rivals Aston Villa.
Saints are seventh, two places and three points outside the play-offs with two matches left.
Blackburn: 26 Mar v Wolves (A) PL2
Southampton: 13 Apr v Fulham (A) PL2