Having lost five of their previous six Premier League matches, confidence was low among David Moyes' squad and that was evident in their play at Goodison Park on Saturday.
But having gone behind to Stephen Hunt's penalty, they showed the character to come from behind and once Phil Jagielka's header had equalised just before half-time the momentum was all in the home team's favour.
However, just when it seemed unlikely they would score again, Wolves defender Stephen Ward gifted them the opportunity seven minutes from time when he pushed over Louis Saha and Leighton Baines stroked home from the spot.
The win will have lifted the mood among the players and supporters alike as discontent about performances on and off the field has been growing in recent weeks.
Prior to kick-off, there had been another march by supporters' group Blue Union to protest about stagnation at the club in relation to finding a new buyer and outside investment which, according to Merseyside Police, numbered about 250.
It was not long before fans inside the ground were complaining about further lack of movement, this time in the opposition penalty area, as a number of crosses from both flanks were sent over with no identifiable target.
However, when one did eventually reach its intended destination in the 16th minute, after Seamus Coleman picked out Tim Cahill, goalkeeper Wayne Hennessey had to be at full-stretch to tip over Saha's shot into the turf from the Australian's knock-down.
Everton continued to struggle with their final ball until late in the first half and they were hit with a classic sucker punch in the 36th minute.
David Edwards' diagonal run across the corner of the penalty area did not appear to pose too much threat but Marouane Fellaini, returning after suspension, caught him with the slightest of touches and it was enough to send the midfielder to the ground.
Hunt smashed home from the spot and it looked like Wolves would hold on to their lead until a minute before the break when Jagielka nodded home Baines' free-kick with a twisting header.
It was only his sixth goal in nearly four-and-a-half years at Everton but, after scoring against Wigan in their last home victory on September 17, this is already his best return in the league for the Toffees.
In added time, Everton could have gone in front but Fellaini's shot was half-saved by Hennessey and Cahill appeared to be pulled back by Karl Henry as he raced to reach the loose ball but referee Jon Moss awarded only a corner.
The home side began the second half positively and Fellaini was first to fire over from range before Cahill's aerial collision with Richard Stearman left the Wolves defender writhing on the Goodison turf and he gingerly left the pitch with what looked like a painful arm or shoulder injury.
Everton were in the ascendancy but were still wasteful in possession, typified by one crossfield pass from John Heitinga which rolled off the end of the pitch - much to the derision of home fans.
But even when they picked out men in position, the Toffees lacked the killer instinct.
Cahill, who has not scored since December 20, looked certain to break his drought when Saha's flick-on from Coleman's cross found him six yards out but he did not connect cleanly and Ward and Hennessey combined to save.
The pressure was building on the visitors and when Saha chested down and shot, his effort was deflected behind.
But from the resulting corner, Ward needlessly fouled the Frenchman to give Baines the chance to coolly side-foot home the penalty.
The goal did little to ease the tension in the final seven minutes though and the final whistle came as a welcome relief for the majority inside Goodison.