The Irons went close to going in front ten minutes into the second period when Bowen took advantage of more loose defending but saw his right-foot shot blocked by Keane. At the other end, Charly Alcaraz twice sliced off-target for the Toffees.
Then, on 64 minutes, Füllkrug showed exactly why he has scored 14 goals for Germany with an unstoppable rapier-like finish into the bottom right-hand corner from the left corner of the penalty area.
After Wan-Bissaka fired into the side netting and Bowen sliced wide, Everton attempted a late rally, but Alcaraz nodded wide, Jake O’Brien’s header was caught by Foderingham and finally Thierno Barry sliced past the post from six yards.
With that, although Lewis Orford was denied by Travers in the final minute, West Ham had a victory in Chicago to celebrate.
The fight for the Premier League Summer Series title will go to the final round of matches in Atlanta on Sunday, where Potter’s side will take on AFC Bournemouth at Mercedes-Benz Stadium at 2pm EDT (7pm BST).
West Ham United: Foderingham, Walker-Peters (Wan-Bissaka HT), Casey (Todibo HT), Mavropanos (Scarles 86), Kilman (Aguerd HT), Diouf (Luis Guilherme HT), Potts (Rodríguez HT), Ward-Prowse © (Bowen HT), Irving (Souček 61), Paquetá (Orford 90), Marshall (Füllkrug HT)
Subs not used: Areola (GK), Golambeckis, Kanté, Fearon, Cornet
Goals: Paquetá 41, Füllkrug 64
Booked: Potts
Everton: Travers, Patterson (Garner HT), Keane, O’Brien, Mykolenko, Armstrong, Gueye © (Tarkowski 70), Iroegbunam (Alcaraz HT), Ndiaye (Chermiti 70), McNeil (Heath 80), Beto (Barry HT)
Subs not used: Pickford (GK), Tyler (GK), Onyango, Thomas, Clarke
Goal: Gueye 17
Booked: Keane, Garner
Referee: Rosendo Mendoza