Aaron Cresswell’s shot deflected off Everton defender Yerry Mina into the path of Soucek, who tapped home in the 85th minute of an uneventful game.
Victory ended a run of four successive defeats at his former club for West Ham manager David Moyes.
Everton, who had won their previous four league games, missed out on climbing to second in the table.
Defences dominate at Goodison
To say the first 85 minutes lacked creativity would be an understatement. Neither side were able to dominate going forward, with the first shot on target coming on the stroke of half-time.
Moyes and Everton manager Carlo Ancelotti have built their teams around defensive stability.
The hosts had conceded only once in four league games before this fixture, while West Ham held Southampton to a goalless draw on Tuesday.
The Hammers had the pick of the chances, Cresswell forcing Jordan Pickford into a smart save and Michail Antonio having a drilled effort kept out in the second half.
West Ham also proved difficult to break down and were playing the better football when midfielder Soucek scored his fifth goal of the season.