diff --git a/patch/Python/_cross_target.py.tmpl b/patch/Python/_cross_target.py.tmpl
index 9f75af5..fbe178f 100644
--- a/patch/Python/_cross_target.py.tmpl
+++ b/patch/Python/_cross_target.py.tmpl
@@ -11,6 +11,8 @@ import sysconfig
 sys.cross_compiling = True
 sys.platform = "{{platform}}"
 sys.implementation._multiarch = "{{arch}}-{{sdk}}"
+sys.base_prefix = sysconfig.get_config_var("prefix")
+sys.base_exec_prefix = sysconfig.get_config_var("prefix")
 
 ###########################################################################
 # subprocess module patches
@@ -67,5 +69,9 @@ def cross_get_sysconfigdata_name():
 sysconfig.get_platform = cross_get_platform
 sysconfig._get_sysconfigdata_name = cross_get_sysconfigdata_name
 
+# Ensure module-level values cached at time of import are updated.
+sysconfig._BASE_PREFIX = sys.prefix
+sysconfig._BASE_EXEC_PREFIX = sys.base_exec_prefix
+
 # Force sysconfig data to be loaded (and cached).
 sysconfig._init_config_vars()