diff --git a/src/cascadia/PublicTerminalCore/HwndTerminal.cpp b/src/cascadia/PublicTerminalCore/HwndTerminal.cpp
index 27775bb314d..3c3e1600192 100644
--- a/src/cascadia/PublicTerminalCore/HwndTerminal.cpp
+++ b/src/cascadia/PublicTerminalCore/HwndTerminal.cpp
@@ -55,10 +55,29 @@ try
 
     if (terminal)
     {
-        if (_IsMouseMessage(uMsg) && terminal->_CanSendVTMouseInput())
+        if (_IsMouseMessage(uMsg))
         {
-            if (terminal->_SendMouseEvent(uMsg, wParam, lParam))
+            if (terminal->_CanSendVTMouseInput() && terminal->_SendMouseEvent(uMsg, wParam, lParam))
             {
+                // GH#6401: Capturing the mouse ensures that we get drag/release events
+                // even if the user moves outside the window.
+                // _SendMouseEvent returns false if the terminal's not in VT mode, so we'll
+                // fall through to release the capture.
+                switch (uMsg)
+                {
+                case WM_LBUTTONDOWN:
+                case WM_MBUTTONDOWN:
+                case WM_RBUTTONDOWN:
+                    SetCapture(hwnd);
+                    break;
+                case WM_LBUTTONUP:
+                case WM_MBUTTONUP:
+                case WM_RBUTTONUP:
+                    ReleaseCapture();
+                    break;
+                }
+
+                // Suppress all mouse events that made it into the terminal.
                 return 0;
             }
         }
@@ -76,6 +95,10 @@ try
             return 0;
         case WM_LBUTTONUP:
             terminal->_singleClickTouchdownPos = std::nullopt;
+            [[fallthrough]];
+        case WM_MBUTTONUP:
+        case WM_RBUTTONUP:
+            ReleaseCapture();
             break;
         case WM_MOUSEMOVE:
             if (WI_IsFlagSet(wParam, MK_LBUTTON))
diff --git a/src/cascadia/TerminalCore/Terminal.cpp b/src/cascadia/TerminalCore/Terminal.cpp
index e7719507099..b71471fc7ef 100644
--- a/src/cascadia/TerminalCore/Terminal.cpp
+++ b/src/cascadia/TerminalCore/Terminal.cpp
@@ -486,14 +486,14 @@ bool Terminal::SendKeyEvent(const WORD vkey,
 // - false if we did not translate the key, and it should be processed into a character.
 bool Terminal::SendMouseEvent(const COORD viewportPos, const unsigned int uiButton, const ControlKeyStates states, const short wheelDelta)
 {
-    // viewportPos must be within the dimensions of the viewport
-    const auto viewportDimensions = _mutableViewport.Dimensions();
-    if (viewportPos.X < 0 || viewportPos.X >= viewportDimensions.X || viewportPos.Y < 0 || viewportPos.Y >= viewportDimensions.Y)
-    {
-        return false;
-    }
-
-    return _terminalInput->HandleMouse(viewportPos, uiButton, GET_KEYSTATE_WPARAM(states.Value()), wheelDelta);
+    // GH#6401: VT applications should be able to receive mouse events from outside the
+    // terminal buffer. This is likely to happen when the user drags the cursor offscreen.
+    // We shouldn't throw away perfectly good events when they're offscreen, so we just
+    // clamp them to be within the range [(0, 0), (W, H)].
+#pragma warning(suppress : 26496) // analysis can't tell we're assigning through a reference below
+    auto clampedPos{ viewportPos };
+    _mutableViewport.ToOrigin().Clamp(clampedPos);
+    return _terminalInput->HandleMouse(clampedPos, uiButton, GET_KEYSTATE_WPARAM(states.Value()), wheelDelta);
 }
 
 // Method Description:
diff --git a/src/interactivity/win32/windowio.cpp b/src/interactivity/win32/windowio.cpp
index 023b14a8598..2b65f515047 100644
--- a/src/interactivity/win32/windowio.cpp
+++ b/src/interactivity/win32/windowio.cpp
@@ -123,7 +123,14 @@ bool HandleTerminalMouseEvent(const COORD cMousePosition,
     // Virtual terminal input mode
     if (IsInVirtualTerminalInputMode())
     {
-        fWasHandled = gci.GetActiveInputBuffer()->GetTerminalInput().HandleMouse(cMousePosition, uiButton, sModifierKeystate, sWheelDelta);
+        // GH#6401: VT applications should be able to receive mouse events from outside the
+        // terminal buffer. This is likely to happen when the user drags the cursor offscreen.
+        // We shouldn't throw away perfectly good events when they're offscreen, so we just
+        // clamp them to be within the range [(0, 0), (W, H)].
+        auto clampedPosition{ cMousePosition };
+        const auto clampViewport{ gci.GetActiveOutputBuffer().GetViewport().ToOrigin() };
+        clampViewport.Clamp(clampedPosition);
+        fWasHandled = gci.GetActiveInputBuffer()->GetTerminalInput().HandleMouse(clampedPosition, uiButton, sModifierKeystate, sWheelDelta);
     }
 
     return fWasHandled;
@@ -635,6 +642,25 @@ BOOL HandleMouseEvent(const SCREEN_INFORMATION& ScreenInfo,
 
         if (HandleTerminalMouseEvent(MousePosition, Message, GET_KEYSTATE_WPARAM(wParam), sDelta))
         {
+            // GH#6401: Capturing the mouse ensures that we get drag/release events
+            // even if the user moves outside the window.
+            // HandleTerminalMouseEvent returns false if the terminal's not in VT mode,
+            // so capturing/releasing here should not impact other console mouse event
+            // consumers.
+            switch (Message)
+            {
+            case WM_LBUTTONDOWN:
+            case WM_MBUTTONDOWN:
+            case WM_RBUTTONDOWN:
+                SetCapture(ServiceLocator::LocateConsoleWindow()->GetWindowHandle());
+                break;
+            case WM_LBUTTONUP:
+            case WM_MBUTTONUP:
+            case WM_RBUTTONUP:
+                ReleaseCapture();
+                break;
+            }
+
             return FALSE;
         }
     }