The Swiss Champions FC Basel, who start their domestic season this week, dominated much of the first half of their game but could not find a way past Marek Stech in the Hammers goal.
In the second half the Hammers conceded after 53 minutes before equalising through Junior Stanislas from the penalty spot.
The game was decided late into added time as Julien Faubert fouled Pak and conceded a penalty converted by Yapi.
Amongst those getting a run out were Kevin Nolan, James Tomkins, Freddie Sears, Luis Boa-Morte and Freddie Piquionne. Carlton Cole also came on for the last 15 minutes.