An import ending in "/" is always an import of a directory.

src/compiler/core.ts

@@ -829,8 +829,20 @@ namespace ts {
     export function normalizePath(path: string): string {
         path = normalizeSlashes(path);
         const rootLength = getRootLength(path);
+        const root = path.substr(0, rootLength);
         const normalized = getNormalizedParts(path, rootLength);
-        return path.substr(0, rootLength) + normalized.join(directorySeparator);
+        if (normalized.length) {
+            const joinedParts = root + normalized.join(directorySeparator);
+            return isPathToDirectory(path) ? joinedParts + "/" : joinedParts;
+        }
+        else {
+            return root;
+        }
+    }
+
+    /** A path ending with '/' refers to a directory only, never a file. */
+    export function isPathToDirectory(path: string): boolean {
+        return path.charCodeAt(path.length - 1) === CharacterCodes.slash;
     }
 
     export function getDirectoryPath(path: Path): Path;

src/compiler/program.ts

@@ -646,7 +646,7 @@ namespace ts {
             trace(state.host, Diagnostics.Loading_module_as_file_Slash_folder_candidate_module_location_0, candidate);
         }
 
-        const resolvedFileName = loadModuleFromFile(candidate, supportedExtensions, failedLookupLocations, onlyRecordFailures, state);
+        const resolvedFileName = !isPathToDirectory(candidate) && loadModuleFromFile(candidate, supportedExtensions, failedLookupLocations, onlyRecordFailures, state);
 
         return resolvedFileName || loadNodeModuleFromDirectory(supportedExtensions, candidate, failedLookupLocations, onlyRecordFailures, state);
     }