Palace thought they had taken a first-half lead through Max Meyer only for Wilfred Zaha, who was wounded up from the opening whistle, to be deemed offside in the build-up by VAR.
Meyer eventually pushed the visitors in front when the defender headed in off the underside of the crossbar from Luka Milivojevic’s free kick five minutes after the restart.
With both sides playing their second game in three days, the goal appeared to be enough but Palace gave Saints a way back into the game.
Martin Kelly’s back pass to James Tomkins was too soft and allowed Ings to swoop in for an easy equaliser.
Southampton found a second wind following the goal and looked most poised to find a winner, but Moussa Djenepo was denied on a spectacular save from Vicente Guaita.
Ings came close to adding a second whilst James Ward-Prowse forced a save from a free-kick, but Saints were unable to find a breakthrough and had to settle for an important point in their march towards safety.
Southampton: McCarthy, Bertrand, Bednarek, Stephens, Cedric, Redmond, Hojbjerg, Ward-Prowse, Boufal (Armstrong 68), Ings, Adams (Djenepo 63)
Unused subs: Gunn (GK), Yoshida, Romeu, Vestergaard, Smallbone
Goals: Ings (74)
Bookings: Ward-Prowse (79)
Crystal Palace: Guaita, Ridewald, Sakho, Tomkins, Kelly, McArthur, Milivojevic, McCarthy, Zaha, Meyer (Kouyate), Ayew
Unused subs: Hennessey (GK), Woods, Wickham, Camarasa, Daly, Pierrick
Goals: Meyer (50)
Bookings: Milivojevic (32), McArthur (85)