Connection systems are disclosed for establishing one or more electrical connections through a drape. An example connection system includes a first connector and a second connector configured to connect to each other. The first connector includes a first-connector housing, an electrical lead extending from the first-connector housing, and at least a first piercing element within the first-connector housing configured to pierce the drape. The first piercing element is orthogonally connected to the electrical lead. The second connector includes a second-connector housing and at least a first receptacle within the second-connector housing. The first receptacle is configured to form at least a first electrical connection of the one or more electrical connections with the first piercing element when the first connector is disposed over the second connector with the drape therebetween. Methods are also disclosed herein for establishing one or more electrical connections through a drape with the connection systems.