Everton grabbed what could be a vital point against Crystal Palace, in a game where they were reduced to ten men away from home, but still find themselves 18th in the league with just six games to go.
The Toffees have never been relegated from the Premier League, but could be set to go down after a number of disappointing seasons.
Their draw at Palace has meant that they are level with Leicester City on points, and are just one point behind Leeds in 16th.
With the table as tight as it is, every point is now crucial. Here's how we think Everton could fare in this final month of Premier League action…
Everton fixtures 27 April: Newcastle (h) 1 May: Leicester (a) 8 May: Brighton (a) 14 May: Man City (h) 20 May: Wolves (a) 28 May: Bournemouth (h) Everton vs Newcastle
Newcastle are in red hot form, fresh from their 6-1 victory over Tottenham, but they will be looking to improve their results on the road, having lost 3-0 at Villa Park in their last away trip.
Everton will hope that home advantage can give them a boost, with Eddie Howe's side still playing for a place in the top four.
The Toffees lost the reverse fixture 1-0 in October, and could face former star Anthony Gordon, who joined Newcastle in January.
Prediction: Everton 0-2 Newcastle
Leicester vs Everton
With both teams dangerously close to relegation, this is arguably the most important game in each of their remaining few.
Win, and Everton can start to put some distance between themselves and the drop zone. Lose, and they may begin to panic about the possibility of going down for the first time in their Premier League history.
Leicester recorded a 2-0 victory at Goodison Park in the reverse fixture, and with the side picking up a victory against Wolves under new interim manager Dean Smith, it will be a game which carries a lot of pressure for the away side.
Everton have won just once away from home in the Premier League all season, but Dyche's men will be right up for it and could come away with a hard-fought point.
Prediction: Leicester 1-1 Everton
Brighton vs Everton
Another tough away game awaits Dyche's side as they travel to face an in-form Brighton side who are in the hunt for a Champions League place.
Brighton ran riot at Goodison Park in January, winning 4-1 with four different goalscorers, and they will hope that Roberto De Zerbi's side aren't as clinical as they were in that match.
With European football still very much in sight for Brighton, they certainly won't be taking their foot off the gas.
Prediction: Brighton 2-0 Everton
Everton vs Man City
Whilst facing Man City is a daunting prospect for anyone, particularly given the form they are in as they chase down Arsenal at the top of the league, Everton may take some comfort that they held Pep Guardiola's side to a 1-1 draw at the Etihad earlier this season.
A Demarai Gray stunner rescued a point for the visitors that day, and they will hope for a similar level of defensive performance as they welcome the likes of Erling Haaland and Jack Grealish to Goodison Park.
City also have a two-legged Champions League semi-final tie against Real Madrid to contend with, and Dyche will hope this means that some of the visitor's star players are rested.
Given the form they are in, it is tough to look past an emphatic City victory.
Prediction: Everton 0-3 Man City
Wolves vs Everton
Wolves could have their safety secured by the time they welcome Everton for their final home game, and the visitors will hope that they have little motivation in what could be a vital game for their survival.
Everton fell victim to a 95th minute winner against Wolves on Boxing Day in Julen Lopetegui's first game in charge, and the Toffees will be out for revenge at Molineux.
Given the potential differences in pressure heading into that game, Everton could walk away with three points, and this could be vital to their hopes of survival given the other tough fixtures they have.
Prediction: Wolves 0-1 Everton
Everton vs Bournemouth
Although Bournemouth have improved in recent months, picking up impressive wins against Liverpool and Tottenham, a 4-0 home defeat to West Ham may affect their confidence in the next few weeks, and their Premier League safety is not yet secure despite being five points clear of Everton.
Everton's final game being at home could be a huge boost, and if they are still within touching distance of safety, they will have to do everything to gain three points in what could be one of the club's most important games in years.
Bournemouth humiliated Everton twice in the space of a week in November as they beat them 4-1 and 3-0 in the Carabao Cup and the League, and Everton will have to be wary of the strength of their opponents going forward.
The Cherries scored twice at Arsenal and three times at Spurs on their travels, but have won just four away games all season, and Everton could use their home advantage to secure victory.
Prediction: Everton 2-0 Bournemouth
Predicted run-in points: 7/18Predicted total points: 35
