They're still going well in the FA Cup, although they had an uncomfortable 2-0 win over non-league Boreham Wood, where they took 57 minutes to break the deadlock.
And in the league, things appeared to be sliding towards relegation until a winner, nine minutes into stoppage time, sealed three points against Newcastle.
They're still in a relegation battle, but now find themselves three points above the drop zone with two games in hand on 18th-place Watford.
Now everyone connected with the club will hope a former Chelsea man can guide the team away from danger. After all, it's happened before.
Everton were close to a first relegation in the 1993/94 season - the second ever Premier League campaign - but were helped out by Graham Stuart, who spent four years at Stamford Bridge before joining the club.
The Toffees entertained a Wimbledon side hell bent on consigning them to what was then the First Division.
The Dons had nothing to play for in a football sense but the 'Crazy Gang' they were notoriously tough to play against.
Things took a dark turn the night before the match as Wimbledon's team bus was set on fire. Thankfully no one was inside the bus at the time.
But it was going to take a bit more than a fire to deter this group of players, who were also looking to do former manager Dave Bassett a favour. Bassett was in charge of Sheffield United, who were also in the relegation dogfight.
Plus, they had the added incentive of a holiday to Las Vegas, paid for by chairman Sam Hammam, Bassett recalled in his book, Settling The Score.
"Sam Hammam felt he had been snubbed once by Everton and wanted to see their demise," he wrote.
With the slot machines of Caesars Palace ringing in their ears, Wimbledon made a perfect start as they raced to a 2-0 lead and Everton looked set for the drop.
Stuart, who moved to Merseyside from Chelsea in 1993, pulled one back with a penalty and then a stunning long-range effort from Barry Horne levelled the match.
Horne's goal changed everything as all of a sudden Sheffield United, Southampton and Ipswich were having to do the maths on who would take up the final relegation spot.
Stuart then netted his second of the match, leaving Everton home and dry, while it was chaos for all the other relegation-threatened clubs.
In an age before smart phones, this inevitably led to lapses in communication, and it was Bassett's Blades who paid the price.
Sheffield United were drawing 2-2 at Chelsea unaware that was enough for them to stay up. In their search for what they thought was a necessary winner they conceded in stoppage time, with defeat confirming they'd join Oldham and Swindon in the drop.
Everton, meanwhile, were on cloud 9 a year later when they beat Manchester United in the 1995 FA Cup final.
Fans, though, will be hoping the situation this term doesn't mirror what happened in 1994. They've been through quite enough already!