James Ward-Prowse missed the chance to put the Saints ahead after firing a penalty against the crossbar after initially winning the spot-kick following a foul from André Gomes.
The visitors went on to break the deadlock just a few minutes later when Ings struck home from close range.
Richarlison brought the home side level with just a few minutes to play in the first-half and it was a goal that came against the run of play.
It was an entertaining game at Goodison, but a point certainly doesn’t suit Everton, whose European dreams are hanging on by a thread.
Story of the game
Fresh from their victory over Manchester City at the weekend, Southampton settled quickly and the visitors had a goal ruled inside eight minutes with Stuart Armstong flagged for offside.
The Blues had their first sight of goal in the 18th minute when they were awarded a free-kick for a foul on Richarlison. Lucas Digne whipped the ball around the wall, but also wide of the post.
Alex McCarthy was called into action just after the drinks break. Anthony Gordon’s cross into the box wasn’t dealt with by the visitors, which allowed Alex Iwobi to get his shot away, which was kept out by the Saints ‘keeper.
Ward-Prowse was involved in the heart of the action around the 27th-minute. His dipping free-kick was tipped over the bar and he almost turned provider when his cross was headed onto the bar by Ings, who beat his marker at the near post.
The Saints skipper was fouled by Gomes in the area just a minute later, but the resulting penalty was rifled against the crossbar by Ward-Prowse.
Southampton didn’t have long to wait for their next opening though and they took a deserved lead just after the half-hour mark. Armstrong drove at the Everton defence and threaded a neat pass through to Ings, whose first touch took the ball away from the advancing Pickford, which left a tap-in for the in-form striker.
Carlo Ancelotti’s side produced a moment of brilliance to draw level right on the stroke of half-time. Digne clipped a delightful 50-yard ball over the Saints back line, which was brought down by Richarlison and the Brazilian struck home against the run of play.
The Saints picked up where they left off and drew a good save from Pickford just a minute into the second-half. Ings’ backheel found Adams, who curls towards goal and the shot was pushed away.
Dominic Calvert-Lewin was picked out by Tom Davies and the striker looked set to pull the trigger, but couldn’t adjust his feet in time. Ancelotti made an adjustment with Davies and Gylfi Sigurdsson sitting in front of the back four and the hosts started to look a lot more comfortable from the hour mark.
There was a moment of real worry for the visitors after Jan Bednarek brought down Richarlison, who had raced down on goal from the halfway line, but after a VAR check, it was deemed the tackle wasn't denying an obvious goalscoring opportunity.
The Saints continued to see more of the ball, but Everton were compact and didn’t allow their opponents to find any gaps in the final third.
Ralph Hasenhüttl’s side pressed for a decisive second goal in the closing stages as Nathan Redmond and Armstrong went close for the visitors, but the home side were content in seeing the game through for a point and they did just that.
Man of the match: Danny Ings
Showed exactly why he’s one of the most talked about strikers in the Premier league at the moment. Never gave Yerry Mina and Michael Keane a moments rest at Goodison. Ings took his goal really well, bringing in the through ball from Armstrong and tapping home. He has taken his goal tally up to 19 this season, in the league, and the Saints marksman looks set to mount a real challenge for the golden boot in the final four games.
Everton’s European dreams hang on by a thread
Ancelotti will have questions to ask of his side, especially in that first hour, after the Blues were second best. Southampton were all over them in the first-half and should’ve really been out of sight if it wasn’t for missed chances. A tactical change saw the home side defend with both Davies and Sigurdsson sitting in front of the back four and they looked happy with a point at the end.
Southampton with plenty of positives to take from draw
The overall feeling for the Saints will be disappointment after not securing all three points. Southampton were the better team for the best part of an hour and certainly looked like scoring against after Ings’ opener. The two sides remain in the bottom half of the table, though, after a point apiece at Goodison.