Dwight McNeil struck a second-half winner as Everton began the processes of clawing back the points they've been deducted with a 1-0 victory at Nottingham Forest, which lifts them up to 18th, two points from safety.
A day after the club launched their appeal against their 10-point deduction for financial issues, Everton extended their impressive away record with a fourth win in five matches on the road in the Premier League.
It seemed boss Sean Dyche would be left to rue Everton's lack of cutting edge in the final third once again after Beto - in for the injured Dominic Calvert-Lewin - blasted a good early opening over the bar and McNeil's shot was cleared off the goal line by Murillo.
But McNeil came up with a moment of quality with his touch and shot across goal to give Everton belief they can pull themselves away from danger, regardless of the outcome of that appeal.
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The result means it's back-to-back home defeats for Forest and their under-pressure head coach Steve Cooper. They have just one win in their last 10 and stay 15th, six points above third-bottom Everton.
However, in a game of fine margins, they will look back on Felipe's shot against a post and a VAR decision not to punish Abdoulaye Doucoure for pulling Ryan Yates' shirt in the penalty box as moments which could have swung the contest their way.
Should Forest have had a penalty?
"It's as blatant a foul as you'd wish to see," Sky Sports' Jamie Redknapp said of Doucoure's shirt-pull on Yates. "It's so important [the officials and VAR] get this right."
It was a decision which left Cooper frustrated. He described it as "a big error". His side had been penalised for a tangle off the ball in the box last week in their defeat to Brighton and Cooper said consistency was lacking from the officials.
"The penalty that was given against us last week, if that's a penalty then the one today is," he said. "That's a frustration. It's a big error and it was last week as well. It's why referees are getting a load of stick.
"We try to help them as much as we can but they've got to help themselves as well."
How Everton grabbed another win on the road...
Everton put Forest under pressure early on with balls into the box, forcing Odysseas Vlachodimos into a nervy punch, testing Willy Boly's aerial defending and then seeing James Garner loop a volley at the goalkeeper.
It led to a golden opportunity for Beto to break through when the unconvincing Vlachodimos and Boly collided, but the forward fired wastefully over. Sean Dyche spun away to face his dugout in despair - he's seen that kind of finishing all too often from his side this season.
Forest struggled to trouble their visitors in the same way, with their first real shot in anger not coming until the half-hour when Anthony Elanga slashed an effort back across goal and just beyond the far post. Morgan Gibbs-White fired their other first-half opening wide on the stroke of half time.
The home side were enjoying more of the possession but it was Everton making the incisions, with Doucoure playing McNeil in for his shot which was brilliantly blocked on the line by Murillo.
The Forest defender and his fellow centre-back Boly had both been struggling with knocks through the half but the young Brazilian showed great awareness and commitment to keep that effort out. Boly would be forced off at the break, though.
His replacement Felipe almost put Forest in front when he fired a loose ball against the woodwork at the start of the second half from a corner. But there was controversy in that move, with Doucoure not punished during a VAR check for pulling Yates' shirt as the cross came in.
The deadlock was finally broken with McNeil's smart touch and finish across Vlachodimos. He had been unfortunate when his first-half effort was blocked on the line but there was no stopping this shot.
The goal galvanised Forest, who threw bodies forwards in search of a leveller. A handball shout against Doucoure was quickly dismissed, with VAR rightly stating he was too close to Gibbs-White when the ball was blasted at him, and there were two excellent stops from Jordan Pickford to deny Elanga and Murillo.
A second yellow for Felipe may have eased Everton's worries but he was fortunate not to be given his marching orders for bringing down Beto and Elanga drew gasps from around the ground when he whipped an 89th-minute shot just past the post. But Everton held on for a crucial three points.
Dyche: This is a restart for us
Everton boss Sean Dyche: "Very pleased. With what's happened over the last few weeks, it's a restart for us. Three away wins on the trot, which is very difficult in the Premier League. The mentality is right and the performance levels are right.
"It's a big step to get that performance after the recent news. We can all talk about the hardship but you've got to keep going. It was a good performance against Manchester United but it was a head-scratcher, and we've had a few of them this season. We've just got to take on the next challenge. The one-game-at-a-time mentality is how I've always approached football."
What's next?
Forest have back-to-back away games over the next week with a trip to Fulham on Wednesday, kick-off 7.30pm, before going to Wolves on Saturday, kick-off 3pm.
Everton play Newcastle at Goodison Park on Thursday, kick-off 7.30pm, and then host Chelsea on Sunday, kick-off 2pm.