LONDON (AP) — After becoming the first team in Premier League history to lose its first seven matches without scoring a goal, recovering Crystal Palace is on the verge of climbing off the bottom of the table.

A win at Brighton on Tuesday in the 14th round will, at least temporarily, move Roy Hodgson's side above Swansea and West Ham, which play on Wednesday against Chelsea and Everton, respectively.

A former England manager, Hodgson was hired on Sept. 12, a day after Palace became the only remaining team in the division without a point. Frank de Boer had been fired, just four games into the season and 77 days after he was appointed.

Hodgson's impact was not instant. His first game in charge was a 1-0 defeat at home to Southampton and was followed by heavy away losses to Manchester City (5-0) and Manchester United (4-0).

However, a win and Palace's first goals of the season came against the most unlikely opponent. Inspired by the return of Wilfried Zaha and a frenzied atmosphere at Selhurst Park, defending champion Chelsea was beaten 2-1.

Palace has remained unbeaten at home since then, drawing 2-2 with both West Ham and Everton, before scoring a last-minute winner to record its second win of the season against Stoke on Saturday.

"When you talk about turning things around, that happened five or six games ago," Hodgson said after Saturday's win, which took Palace's tally to eight points after 13 rounds.

"We've turned things around enormously and given some very good performances but we haven't always been rewarded with the victories. I don't want to say that this is the catalyst for lots and lots of victories. What it means is that we know what we've got to do for the next 25 games."

When Hodgson took over, he was without Zaha and soon lost first-choice striker Christian Benteke. Zaha is now finding his best form and, having returned earlier in November, Benteke has begun to make an impact from the bench.

Buoyed by impressing on his international debut, Chelsea loan Ruben Loftus-Cheek underscored his progress by grabbing his first goal of the season against Stoke, while Andros Townsend is benefiting from having more quality around him.

The short trip south to promoted side Brighton represents a good opportunity for Palace to capture its first away point and goal this season and more winnable games follow. Four of the Eagles' following five matches are against teams in the bottom half of the table.

And in Hodgson, Palace has a manager that has avoided Premier League relegation from a perilous position before. Trailing 2-0 at Man City in April 2008 and set to be relegated, Hodgson's Fulham side came back to win 3-2 before winning its final two games of the season to stay up.

"We were out of the league for a long, long time," said Hodgson of that campaign with Fulham. "I'd like us to climb out of our hole a bit quicker than Fulham were able to climb out of theirs."

Here's what else to watch out for this week:

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RECORD-BREAKING CITY

Manchester City can set a club record by winning a 12th straight league game when it hosts Southampton on Wednesday.

Pep Guardiola's side equaled a record set between April and September 2015 by defeating Huddersfield 2-1 on Sunday. The win saw City move to 37 points from 13 games — the highest ever points total at this stage of a Premier League season.

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MOYES RETURNS

Unlike Palace, Everton and West Ham have yet to see any major improvements after firing their managers.

David Moyes did claim his first point since replacing Slaven Bilic as Hammers manager, drawing 1-1 with Leicester on Friday. He will now look to build on that as he returns on Wednesday to the club he managed for 11 years.

Moyes has failed to last more than a year in stints with Manchester United, Real Zaragoza and Sunderland since leaving Goodison Park in 2013.

Everton is in freefall after a 4-1 loss to Southampton on Sunday. David Unsworth has been in temporary charge since Ronald Koeman was fired on Oct. 23, but has managed just one win during his seven-game tenure. The club is still searching for a permanent replacement, with Unsworth's failure to improve results likely having ruled him out.