diff --git a/src/corePlugins.js b/src/corePlugins.js
--- a/src/corePlugins.js
+++ b/src/corePlugins.js
@@ -741,11 +741,19 @@ export let corePlugins = {
   zIndex: createUtilityPlugin('zIndex', [['z', ['zIndex']]], { supportsNegativeValues: true }),
   order: createUtilityPlugin('order', undefined, { supportsNegativeValues: true }),
   gridColumn: createUtilityPlugin('gridColumn', [['col', ['gridColumn']]]),
-  gridColumnStart: createUtilityPlugin('gridColumnStart', [['col-start', ['gridColumnStart']]]),
-  gridColumnEnd: createUtilityPlugin('gridColumnEnd', [['col-end', ['gridColumnEnd']]]),
+  gridColumnStart: createUtilityPlugin('gridColumnStart', [['col-start', ['gridColumnStart']]], {
+    supportsNegativeValues: true,
+  }),
+  gridColumnEnd: createUtilityPlugin('gridColumnEnd', [['col-end', ['gridColumnEnd']]], {
+    supportsNegativeValues: true,
+  }),
   gridRow: createUtilityPlugin('gridRow', [['row', ['gridRow']]]),
-  gridRowStart: createUtilityPlugin('gridRowStart', [['row-start', ['gridRowStart']]]),
-  gridRowEnd: createUtilityPlugin('gridRowEnd', [['row-end', ['gridRowEnd']]]),
+  gridRowStart: createUtilityPlugin('gridRowStart', [['row-start', ['gridRowStart']]], {
+    supportsNegativeValues: true,
+  }),
+  gridRowEnd: createUtilityPlugin('gridRowEnd', [['row-end', ['gridRowEnd']]], {
+    supportsNegativeValues: true,
+  }),
 
   float: ({ addUtilities }) => {
     addUtilities({

diff --git a/tests/negative-prefix.test.js b/tests/negative-prefix.test.js
--- a/tests/negative-prefix.test.js
+++ b/tests/negative-prefix.test.js
@@ -360,3 +360,27 @@ test('addUtilities without negative prefix + variant + negative prefix in conten
 
   expect(result.css).toMatchCss(css``)
 })
+
+test('negative col/row-start/end utilities', () => {
+  let config = {
+    content: [{ raw: html`<div class="-col-start-4 -col-end-4 -row-start-4 -row-end-4"></div>` }],
+    corePlugins: { preflight: false },
+  }
+
+  return run('@tailwind utilities;', config).then((result) => {
+    expect(result.css).toMatchCss(css`
+      .-col-start-4 {
+        grid-column-start: -4;
+      }
+      .-col-end-4 {
+        grid-column-end: -4;
+      }
+      .-row-start-4 {
+        grid-row-start: -4;
+      }
+      .-row-end-4 {
+        grid-row-end: -4;
+      }
+    `)
+  })
+})

Col-end does not support negative values
This is a very small issue, col-end does not support negative values out of the box, but negative values makes a lot of sense there. This happens on **v3.4.3**.

https://play.tailwindcss.com/8L8o0VhDfr

The code is here:

~~~ html
<div class="grid grid-cols-3">
  <div class="-col-end-1">BROKEN</div>
  <div class="col-end-[-1]">WORKS</div>
</div>
~~~

I'm not sure if this is exactly a bug, because it is not explicitly described in the documentation, but it is a broken expectation (I've expected that to work for consistency).

tests/negative-prefix.test.js