Notably, the pink protest cards were out in force by the Everton faithful again this week.
There was little to choose between the sides during the opening exchanges, although Anthony Elanga looked like the most dangerous player on the pitch over the first 20 minutes, with Ashley Young struggling to keep up with the 21-year-old.
However, the first big chance of the match fell the way of the Toffees when Odysseas Vlachodimos dropped a high ball into the box that fell at the feet of Beto, but the forward skied his first-time effort over the bar from roughly 12 yards out.
Forest had their first real sight of goal at the half-hour mark, with Elanga getting on the end of a cross into the box, but the forward was unable to guide the ball inside the far post with his attempt.
The best chance of the first half went the way of the visitors when Abdoulaye Doucoure played in McNeil, who put his shot past Vlachodimos, but Murillo got back on the line and cleared the ball to safety off the face of the upright.
It was all square at the interval, but Everton should probably have been in the lead with two big chances wasted.
Forest made a bright start to the second half and almost got the opening goal with a shot from Felipe that struck the woodwork.
Amid the tussle in the box during that attempt, Doucoure looked to have pulled Yates to the ground, which the referee waved on, and after a VAR review, the video assistants decided there was not enough evidence to overturn the onfield decision.
Unfortunately for Forest, their frustrations were increased 10 minutes later as Beto miscued a header in the opposing box that fell to McNeil, who lashed a powerful shot into the top corner to give the Toffees the lead.
Elanga almost pulled his side level twice in the final 10 minutes but saw his first attempt smothered by Jordan Pickford, while his second went just wide of the far post from a snap-shot, but Everton parked the bus in stoppage time and saw the game out for a big three points.
Forest will head to Craven Cottage in midweek to take on Fulham, while Everton welcome Newcastle United to Goodison Park on Thursday night.No Data Analysis info