Sadly, it did not remain that way for long and by the midway point of the second half Tottenham were out of sight and West Ham were down to ten men.
After Bowen had shot wide, an unmarked Sarr powered in Xavi Simons’ corner at the far post less than two minutes in.
West Ham briefly rallied, with Vicario saving from Bowen and catching Diouf’s header, and Kilman heading over, but the game was soon over.
On 55 minutes, Souček’s chest control let him down and, in his eagerness to recover, he slid and caught Palhinha high on the shin. Gillett immediately showed the Czech a red card on his 250th appearance for the Club.
Within 90 seconds, Romero picked out Lucas Bergvall and the Swede sent a header looping over Hermansen and into the net.
Then, minutes after Potter had sent on Soungoutou Magassa for his debut, teenager Bergvall squared and van de Ven swept home a third.
The remainder of the game was, predictably, played in the home half as the ten men in Claret and Blue sought to keep the score down, and Hermansen and substitute Andy Irving did their bit in added-time, both denying Kudus a goal on his return.
West Ham United: Hermansen, Walker-Peters, Mavropanos, Kilman, Diouf, Fernandes (Magassa 61), Ward-Prowse (Irving 90+1), Souček, Summerville (Luis Guilherme 61), Bowen ©, Paquetá (Wilson 68)
Subs: Areola (GK), Wan-Bissaka, Igor, Potts, Füllkrug
Sent-off: Souček 55
Tottenham Hotspur: Vicario, Porro, Romero ©, van de Ven (Danso 80), Spence (Udogie 71), Palhinha, Bergvall (Johnson 80), Sarr, Kudus, Simons (Richarlison 71), Tel (Odobert 79)
Subs: Kinský (GK), Davies, Bentancur, Kolo Muani
Goals: Sarr 47, Bergvall 57, van de Ven 64
Booked: Spence
Referee: Jarred Gillett
Attendance: 62,459