Wayne Rooney did his best to wreck Steve Wigley's first game in charge of Southampton - but Fabrice Fernandes earned Saints' caretaker boss a debut point with a stunning stoppage-time equaliser.
Southampton fans protested in the stands prior to kick-off against the rumoured return of Glenn Hoddle.
The demonstration clearly affected the Saints players and the home side found themselves two goals down almost before Wigley had found his way to the touchline.
Rooney should have opened the scoring after just four minutes when he shot narrowly wide from ten yards after the home defence had failed to deal with Kevin Kilbane's cross.
But Wigley, who was handed temporary control following Gordon Stachan's resignation last week, did not have to wait long to see his side concede the first goal of his managerial career.
Rooney seized on Claus Lundekvam's under-hit back pass before smashing Everton into the lead with a 20-yard shot, which deflected in off Michael Svensson.
The Toffees teenager should have scored again 12 minutes later when he side-footed wide with only goalkeeper Antti Niemi to beat after getting in behind the Southampton defence once more.
Everton did finally make their territorial advantage tell 13 minutes before half time when Duncan Ferguson headed the second goal.
Danish international Thomas Gravesen picked out Ferguson with a pinpoint cross and the big striker planted a looping header beyond Niemi and into the left-hand corner of the net.
Ferguson should have put the game beyond doubt on the stroke of half time when, following dazzling footwork from Rooney, he fired over the crossbar with only Niemi to beat.
Stand-in boss Wigley was forced into the first major decision of his fledgling managerial career when he brought on top-scorer James Beattie and Fernandes as half-time substitutes.
The changes paid dividends almost instantly as Fernandes shot over from the edge of the area within minutes of coming on.
Saints were back in the game on the hour when Kevin Phillips volleyed the first goal of Wigley's reign.
Svensson headed a David Prutton cross into Phillips' path, before the former England striker drilled home from six yards out.
Rooney restored Everton's two-goal advantage 12 minutes from time when he completed his brilliant brace.
The England striker beat four home defenders before exchanging passes with Steve Watson and finding the corner of the net with a bullet shot from ten yards.
Saints were handed the chance to cut the deficit three minutes later when referee Phil Dowd awarded a controversial penalty.
Prutton was hacked down by Everton's Tobias Linderoth and Dowd pointed to the spot, although television replays showed that the challenge was a yard outside the area.
Beattie did not let the protests hamper him and calmly made it 3-2 from the spot.
Saints completed a remarkable fightback when the impressive Fernandes equalised with his first goal of the season.
The Frenchman picked up the ball on the right edge of the penalty area before cutting in and unleashing an unstoppable left-foot shot that curled in off the right post.
Everton boss David Moyes afterwards lavished praise on Rooney, but admitted the teenager should have scored the first hat-trick of his career.
He said: "Wayne was very impressive but if I was being negative I would say he should have scored more goals.
"We should have killed them off in the first half when we could have been three or four up.
"We let them back in the game but when we made it 3-1 I thought we would see out the victory.
"I thought we deserved to win the match but things conspired against us. I've seen the penalty and the challenge took place outside the box but that's football.
"If we keep on playing as well as that then there is no danger of us getting relegated." A delighted Wigley said: "In the first half we were shocking and we could only get better after the break.
"At least at half time there was a chance to compose myself and restore a bit of sanity.
"I did not even need to say much at the break because we all knew where we had been going wrong.
"Our headers were poor, so were our tackles and every time we passed the ball it seemed to go to an Everton player.
"It was a time to get back to honest hard work and to do the things which made us such a good team in the past.
"We were much better in the second half and at least our supporters had something to cheer. At half time I reckon many of them would have been happy to go home.
"In the second half we looked like a football team again and James Beattie was typical of the way we played.
"James made a huge difference after I had left him out of the starting line-up. I have learned this week that he is a top-class person, as well as a player.
"When I picked the team I kept Brett Ormerod and Kevin Phillips as our attackers and I felt they had deserved their chicane. Any other decision would have been disrespectful.
"I learned a lot today. When you are running the youth team you could hide behind the development tag, but here there is no place to hide.
"I accept that at half time the fans would have been glad if we had brought in a new manager there and then and I could not have disagreed.
"But I am not going to put in for the job no matter what happens in subsequent matches.
"I am in charge while the chairman and board of directors are interviewing and I hope they take their time and make the best decision in the interests of the club.
"They have not done badly over the last six or seven years in their choice of managers and whoever gets the job will inherit a wonderful position.
"The club has moved forward and we have a great stadium and some top class players so I hope we do not rush into anything." Man of the Match: Wayne Rooney Two goals and there could have been at least another two. His performance deserved to be on the winning side and Everton should have gone home with three points.