Swansea moved out of the relegation zone as they comfortably dispatched a dismal West Ham side whose performance was so "embarrassing" manager David Moyes said it was "impossible to assess".
Ki Sung-Yeung shot low into the corner from Andre Ayew's pass to open the scoring inside 10 minutes, before Mike van der Hoorn nodded in the South Korean's corner amid slack marking.
Between those two first-half goals, Winston Reid was put in a neck brace and taken off on a stretcher after suffering a bad injury in a goalmouth scramble.
He received treatment for 10 minutes after appearing to be knocked unconscious and was taken to hospital for a scan.
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After the break, West Ham crumbled further. Andy King tapped in the rebound from an Adrian save that denied Andre Ayew's header from another corner, before Cheikhou Kouyate tripped Ayew in the box.
Andre's brother Jordan Ayew coolly slotted the spot-kick into the corner to round off a vital win that was only slightly dampened by Michail Antonio's late consolation, the substitute winger finishing from Aaron Cresswell's delivery.
"The fans travelled through the snow to get here and we let them down badly," Moyes added.
"We had no intensity in our play, we thought we could just stroll about."
Meanwhile, Carlos Carvalhal's impressive work continues. His team are now up to 13th in the table - climbing above the Hammers on goal difference - having been bottom when he took over in late December. This was a seventh consecutive home win in all competitions.
West Ham drop to 14th, with both sides still only three points clear of the bottom three.