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.
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.