Manchester United's run of six wins in a row came to an end when they were beaten 2-1 by Tottenham on New Year's Day, their sixth Premier League defeat of the season and their fourth at home.
Moyes is likely to rest players ahead of United's Capital One Cup semi-final with Sunderland on Tuesday, but another defeat at Old Trafford will see the pressure mount even further.
Here's a list of key tactical battles that could shape Sunday's game.
Rio Ferdinand v Wilfried Bony
In the absence of Michu, Wilfried Bony is likely to lead the line for Swansea at Old Trafford. The Ivorian striker was on the losing side against Manchester City on New Year's Day but he gave centre-halves Vincent Kompany and Matija Nastasic a rough afternoon, scoring both Swansea's goals.
Jonny Evans and Nemanja Vidic didn't cope well with the strength and movement of Roberto Soldado and Emmanuel Adebayor against Tottenham, and Rio Ferdinand, who returned to the bench last week, will have to do a better job of keeping Bony quiet.
He will rely on his full-backs to stop crosses at the source, but he has to do his bit by keeping tight and not letting Bony get across him when the ball does make it into the box.
Tom Cleverley and Ryan Giggs v Jose Canas, Leon Britton and Jonjo Shelvey
Whoever plays in midfield for United is likely to be outnumbered. Moyes will have to do without Wayne Rooney and Robin van Persie, but he's played with two strikers in each home game this season.
If the United manager follows the same pattern, then Danny Welbeck and Javier Hernandez will start up front with two, rather than three, men in central midfield.
Jonjo Shelvey will be the furthest forward of Swansea's midfield three and looking to find space between United's defence and midfield. Ryan Giggs and Tom Cleverley will need to communicate with their centre-halves and pass him onto them whenever they can.
Javier Hernandez v Ashley Williams
Javier Hernandez looked isolated when he started as a lone striker against Norwich, but he's likely to have Danny Welbeck for company against Swansea.
Welbeck's physical presence will allow Hernandez to do what he does best: play on the shoulder of the last defender, run in behind Swansea's back four and get on the end of chances in the penalty area.
Ashley Williams is quick, but he hasn't got the pace to live with Hernandez if United's midfield can find him with passes behind Swansea's defence.
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