United are through to the fifth round of the FA Cup and are flying high in seventh in the league, nine points better off than a Palace side with one win in their last nine overall.
The Hammers kept their momentum going with a comfortable 4-0 win over Doncaster Rovers in the FA Cup on Saturday - the first time they have scored three or more in a home tie in the competition in a decade.
Everything is looking up for David Moyes, who has not been afraid to tweak his system to get the most out of his squad.
A victory on Tuesday would make it the first time that the Scotsman has won four successive Premier League games since December 2013 when in charge of Manchester United. It is a feat West Ham last managed in December 2018.
Three league wins in a row for West Ham, most recently seeing off West Bromwich Albion 2-1, has them within two points of fourth-placed Liverpool and dreaming of a place in Europe.
With a home match against stuttering champions Liverpool to come next week, Moyes will be keen to get three more points on the board on Tuesday against cross-city rivals Palace.
The Eagles have struggled for momentum pretty much all season long, though they have taken points off Tottenham Hotspur, Leicester City and Arsenal over the past five weeks.
Last week's heavy 4-0 reverse at the hands of Manchester City would have dented confidence, though, with Palace now marooned in mid-table, neither in relegation danger nor in serious European contention.
Hodgson's men have failed to win any of their last 19 games against teams starting the day in the top half, as is the case for West Ham, with their only four wins since September 19 coming against the three promoted clubs and bottom side Sheffield United.
If they are to get their campaign back on track then goals are needed. Since beating West Brom 5-1 at the start of December, Palace have scored just five more goals in eight league games, failing to find the net four times in that run.
The good news for the Eagles is that they are unbeaten in their last four top-flight encounters with West Ham, winning two and drawing two, a run that includes a 1-1 draw when the sides faced off a little over a month ago.
Crystal Palace Premier League form: LLDWDL
Crystal Palace form (all competitions): LDWLDL
West Ham United Premier League form: LDDWWW
West Ham United form (all competitions): DWWWWW
The hosts have had a week-and-a-half rest between games but changes may still be made on the back of the loss to Man City, including a possible return for Christian Benteke up top.
Fabian Balbuena is back in contention for United, but Moyes may stick largely with the same side that beat West Brom last time out in the league.
Michail Antonio, rested for the cup win against Doncaster, has scored the winning goal in West Ham's last two Premier League victories - the last player to score the winner in three consecutive top-flight games for the Hammers was Bobby Zamora in 2007.
Crystal Palace possible starting lineup:
Guaita; Ward, Kouyate, Tomkins, Mitchell; Townsend, McArthur, Milivojevic, Eze; Zaha, Benteke
West Ham United possible starting lineup:
Fabianski; Coufal, Dawson, Ogbonna, Cresswell; Rice, Soucek; Bowen, Benrahma, Fornals; Antonio
We say: Crystal Palace 1-2 West Ham United
West Ham have looked very impressive in recent weeks and have a serious shout of playing European football next season if they can keep their momentum going.
Palace have had plenty of time to ponder their heavy loss to Man City last time out, but given their home league record - two wins in eight - we are backing United to take all three points.
Top betting tip
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