The Hammers returned to Europa League action on Thursday night after their Europa Conference League win last season, but fell behind early in the second half.
It came when Angelo Ogbonna was caught napping at the back and Petar Stanic fired Backa Topola in front.
West Ham fans were left shocked after falling behind but were eventually able to find a response.
Said Benrahma pulled off an excellent run down the left and sent a teasing ball into the box towards Kudus.
It looked as though he was the scorer in the 66th minute but it went down as a Nemanja Petrovic own-goal.
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Moments later though, Kudus did in fact score his first goal for the Hammers as he headed in from James Ward-Prowse' corner.
Ward-Prowse turned provider again as his corner from the left found Tomas Soucek's, whose glancing header put the Hammers 3-1 up.
Backa Topola showed great energy for the remaining moments of the game after their impressive efforts earlier on.
However, West Ham's quality inevitably shined through and they went on to secure all three points in the group.
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It's a game that has seen Ward-Prowse further add to his goal contribution tally for the club.
He has now scored twice and assisted five other goals in his opening five matches in east London, a hugely impressive start.
German side Freiburg and Greek outfit Olympiacos are West Ham's other two opponents in Group A as they eye another piece of European silverware.
CSKA Moscow 
FC Rostov 
Leicester 
Chelsea 
Valencia 
Betis 
Dynamo Kyiv 
Chornomorets Odesa 
Verona 
Inter 
Bayer Leverkusen 
FC Heidenheim 
Borussia Dortmund 
SC Freiburg 
VFL Wolfsburg 
Union Berlin 
Arsenal 
Nottingham Forest 
Everton 
Brentford 
Spartak Moscow 
Lokomotiv Moscow 
Rangers 
Dundee Utd 
Atletico Madrid 
Alaves 
Lens 
Marseille 
Ingulets Petrove 
Shakhtar Donetsk 
AC Milan 
Juventus 
ST Malo 
Bordeaux 
Manchester City 
Tottenham 
Eintracht Frankfurt 
Werder Bremen 
Girona 
Espanyol 
Feyenoord 
Heerenveen 
ST Etienne 
Montpellier 
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Heart Of Midlothian 
Celtic 
Reims 
Lyon 
PSV 
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Celta Vigo 
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Estrela Da Amadora 
Sparta Rotterdam 
AZ Alkmaar 
Southampton 
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