diff --git a/request.go b/request.go
index 7c08b21..b655648 100644
--- a/request.go
+++ b/request.go
@@ -5,6 +5,7 @@ import (
 	"encoding/base64"
 	"fmt"
 	"net/http"
+	"net/textproto"
 	"net/url"
 	"strconv"
 	"strings"
@@ -60,7 +61,7 @@ func NewRequest(ctx context.Context, e events.APIGatewayProxyRequest) (*http.Req
 	}
 
 	for k, values := range e.MultiValueHeaders {
-		req.Header[k] = values
+		req.Header[textproto.CanonicalMIMEHeaderKey(k)] = values
 	}
 
 	// content-length
diff --git a/response.go b/response.go
index 22c6664..4e14b07 100644
--- a/response.go
+++ b/response.go
@@ -63,6 +63,7 @@ func (w *ResponseWriter) WriteHeader(status int) {
 	for k, v := range w.Header() {
 		if len(v) == 1 {
 			h[k] = v[0]
+			mvh[k] = v
 		} else if len(v) > 1 {
 			mvh[k] = v
 		}