The Saints have won their last two - including a 2-0 success at Chelsea on Boxing Day - to rise into 14th in the table, while a solid campaign to date has left Palace in ninth position with 26 points.
Southampton did not win a single match in any competition between September 28 and November 23, at which point the club's owners must have been tempted to change their manager in order to reset.
The Saints have now won four of their last six in the Premier League, though, including back-to-back victories over Aston Villa and Chelsea in their last two top-flight outings.
Thursday's two-goal success at Stamford Bridge was hugely impressive, and the result saw Ralph Hasenhuttl's side end Boxing Day in 14th position in the table, three points clear of the bottom three.
There is still a long way to go this season, but the team's form and indeed performances in recent weeks suggests that they will have enough to secure another campaign of top-flight football.
Southampton have also won three of their last five Premier League meetings with Palace, suffering just one defeat in the process. That said, the loss during that run came at St Mary's in January 2018.
A record of 26 points from 19 Premier League matches has left Palace in ninth position in the table. They have won seven of their 19 league games this term, which is the same number as Manchester United and Sheffield United, and indeed more than Wolverhampton Wanderers.
Hodgson's side entered Thursday's clash with West Ham United off the back of a three-game winless run, but they turned things around against the Hammers to pick up an important 2-1 win.
Palace now face back-to-back away matches against Southampton and Norwich City before hosting Arsenal and travelling to Manchester City. The capital side will also begin their FA Cup challenge for the 2019-20 campaign with a home game against Championship side Derby County on January 5.
It seems unlikely that the Eagles will be dragged into a relegation battle this season, although in terms of this match, they have only won twice against Southampton since January 2016, suffering five defeats in the process.
Palace have been impressive on their travels this season, though, triumphing at Burnley, West Ham and Manchester United thus far during the 2019-20 campaign.
Southampton Premier League form: WWLLWW
Crystal Palace Premier League form: WWDDLW
Danny Ings started on the bench against Chelsea due to the sheer volume of matches during this stage of the season, but the striker, who has scored 11 Premier League goals this season, is expected to return to the starting XI this weekend.
As for Palace, Patrick van Aanholt is set for another spell on the sidelines after picking up a thigh injury against West Ham, while Christian Benteke, Scott Dann, Joel Ward, Gary Cahill, Jeffrey Schlupp and Andros Townsend remain on the treatment table.
Jairo Riedewald should also come in for fellow Dutchman Van Aanholt at left-back.
Southampton possible starting lineup:
McCarthy; Cedric, Stephens, Bednarek, Bertrand; Armstrong, Ward-Prowse, Hojbjerg, Redmond; Ings, Obafemi
Crystal Palace possible starting lineup:
Guaita; Kelly, Tomkins, Sakho, Riedewald; Milivojevic, Kouyate, McArthur; Zaha, Ayew, Meyer
We say: Southampton 2-1 Crystal Palace
Palace's squad is seriously stretched at the moment, and the quick turnaround in matches makes it even tougher for the Eagles. Southampton, on the other hand, will be full of confidence following their win at Chelsea. We just fancy Hasenhuttl's side to shade what is likely to be close game on the south coast.