Although they have been indifferent on the road in recent times, if the Londoners can pick up a victory against Carlos Carvalhal's men, their prospects for the rest of the season will look much more secure.
Jordan Ayew heaped more misery on Moyes with a penalty after his brother Andre, making his first start for Swansea since rejoining the club from the Hammers in January, was brought down by Cheikhou Kouyate.
Reid was then hurt following an awkward fall when clearing a Swansea corner.
He received treatment for 10 minutes after appearing to be knocked unconscious, and was taken to hospital for a scan.
Reid attempted to make a last-ditch tackle on Swansea's Mike van der Hoorn before getting his foot stuck in the ground and forcefully twisting his knee. "Hopefully that freedom in the second half is something we can carry on".
West Ham fans will be seeing it as one they should win, despite the enforced changes for Moyes.
The win made it a fourth successive Premier League win at home for the first time since May, 2016, and it meant they notched a seventh victory in a row at the Liberty Stadium in all competitions for the first time since November, 2004. Pic: Mark Kerton/PA Wire. Pic: John Walton/PA Wire.
The South Korean produced two neat finishes, from Dele Alli and Harry Kane assists respectively, to take Spurs five points ahead of fifth-placed Chelsea in the table.
Son struck again in the 54th minute, timing his run perfectly to meet Harry Kane's cross with a bullet header past Huddersfield goalkeeper Jonas Lossl.
Riyad Mahrez rescued Leicester with a last-gasp equaliser in their 1-1 draw against Bournemouth.
Turkey forward Cenk Tosun had put the visitors in front after 20 minutes with his first goal in English football.
"It was a thorough performance and winning one", Burnley manager Sean Dyche said.
To compound Everton's woe, Ashley Williams was sent off late in the second half for an elbow on Barnes.