Manchester City were held to a shock goalless draw by relegated Southampton Saturday, slowing the charge for a Champions League spot as Brentford and Brighton and Hove Albion kept up their push for European qualification.
The point for Southampton takes them to 12 for the season, meaning they have avoided the tag of being the joint-worst team in Premier League history.
They are now one point clear of Derby's tally of 11 in the 2007/08 campaign.
Despite the draw, third-placed City remain well-placed to finish in the top five, which would secure qualification for the Champions League next season.
With two games to play they are four points clear of sixth-placed Nottingham Forest, though their rivals all have a game in hand.
City's title defence came off the rails in November and December during a season that Guardiola has admitted has been the toughest of his 16-year managerial career.
The away side dominated possession at St Mary's Stadium and had 26 shots but managed just five on target during a frustrating afternoon.
Saints had picked up just two points out of a possible 33 in their previous 11 games and were given little chance of getting anything from the match.
Brentford beat already relegated Ipswich Town 1-0 for their fourth straight win, climbing to eighth in the table, which may be enough for European football next season.
Kevin Schade headed home from Bryan Mbeumo's corner in the 18th minute for his 11th Premier League goal of the season.
Brighton, also chasing European football, beat Wolverhampton Wanderers 2-0 at Molineux and are behind Brentford only on goal difference.
Danny Welbeck scored a first-half penalty and Brajan Gruda added a second in the 85th minute to secure the three points.
Everton went into their match on a poor run of form following a sharp uptick when David Moyes returned to manage the club but they have long reached safety in the top flight.
Raul Jimenez put mid-table Fulham ahead at Craven Cottage but Vitalii Mykolenko levelled on the stroke of half-time.
Two second-half goals in three minutes from Michael Keane and Beto made it 3-1.
Aston Villa travel to Bournemouth in the Saturday evening kick-off, still dreaming of securing a Champions League spot for next season.
Fourth-placed Newcastle United host Chelsea, a place below them, Sunday, with Forest in action against relegated Leicester City.
Champions Liverpool play Arsenal, who are not yet certain of finishing in the top five despite being the closest challengers to Arne Slot's men this season.
RESULTS
Fulham 1 (Jimenez 17) Everton 3 (Mykolenko 45+3, Keane 70, Beto 73)
Ipswich 0 Brentford 1 (Schade 18)
Southampton 0 Man City 0
Wolves 0 Brighton 2 (Welbeck 28-P, Gruda 85)
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