The Hammers came from behind to beat Silkeborg, keeping their perfect record in Group B.
The visitors dominated in Demark but fell behind when Kusk scored his first goal.
The Hammers were able to tie the game eight minutes later after Lanzini was awarded a penalty.
In the 25th minute, Gianluca scamacca completed the comeback for the Hammers, who were three up at the half-time break.
Silkeborg set up a tense finale with 15 minutes to go when Soren Tengstedt scored on the rebound of Tonni Adamsen's shot after the ball had been thrown.
The hosts were denied a point in the group stage of the European competition.
In the other fixture of the group, Anderlecht were held to a draw by CFRB.
This was the fourth successive win in Europe for David Moyes' side, who have had a poor start to the season.
The Hammers were heavy favorites against the side who finished third in the Superliga.
They were behind for a second match in a row and could have been behind at the break.
Nicklas Helenius headed into an empty net after the referee gave a soft free-kick for a foul on West Ham goalkeeper Alphonse Areola.
After the Hammers went into a two-goal lead, Silkeborg came back with a counter- attack from a Hammers corner.
The Danes had a chance to level the game in the 80th minute, but they couldn't find a way to score, and West Ham held on.
Next up for the team is a trip to Anderlecht, who are in second place.
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