diff --git a/src/requests/adapters.py b/src/requests/adapters.py
index 9a58b16025..b4cc4e6505 100644
--- a/src/requests/adapters.py
+++ b/src/requests/adapters.py
@@ -472,6 +472,17 @@ def get_connection_with_tls_context(self, request, verify, proxies=None, cert=No
             )
         except ValueError as e:
             raise InvalidURL(e, request=request)
+
+        # If request has a Host header, use its value as the server_hostname for SNI
+        server_hostname = None
+        if 'Host' in request.headers:
+            server_hostname = request.headers['Host']
+        elif 'host' in host_params:
+            server_hostname = host_params['host']
+
+        if server_hostname:
+            pool_kwargs['server_hostname'] = server_hostname
+
         if proxy:
             proxy = prepend_scheme_if_needed(proxy, "http")
             proxy_url = parse_url(proxy)
diff --git a/tests/test_adapters.py b/tests/test_adapters.py
index 6c55d5a130..080c8075a6 100644
--- a/tests/test_adapters.py
+++ b/tests/test_adapters.py
@@ -1,4 +1,8 @@
+import unittest
+from unittest import mock
+
 import requests.adapters
+from requests.models import PreparedRequest
 
 
 def test_request_url_trims_leading_path_separators():
@@ -6,3 +10,61 @@ def test_request_url_trims_leading_path_separators():
     a = requests.adapters.HTTPAdapter()
     p = requests.Request(method="GET", url="http://127.0.0.1:10000//v:h").prepare()
     assert "/v:h" == a.request_url(p, {})
+
+
+class TestHTTPAdapter(unittest.TestCase):
+    def test_get_connection_with_tls_context(self):
+        """Test that get_connection_with_tls_context correctly passes server_hostname."""
+        adapter = requests.adapters.HTTPAdapter()
+        
+        # Case 1: Request with a custom 'Host' header (custom SNI)
+        mock_request = mock.MagicMock(spec=PreparedRequest)
+        mock_request.url = "https://1.2.3.4:5678/api/check"
+        mock_request.headers = {'Host': 'custom.hostname.com'}
+        
+        # Mock the pool managers
+        adapter.poolmanager = mock.MagicMock()
+        adapter.proxy_manager = {}
+        
+        # Test without proxy
+        adapter.get_connection_with_tls_context(mock_request, verify=True)
+        
+        # Verify that poolmanager.connection_from_host was called with server_hostname
+        called_args = adapter.poolmanager.connection_from_host.call_args[1]
+        self.assertIn('pool_kwargs', called_args)
+        self.assertIn('server_hostname', called_args['pool_kwargs'])
+        self.assertEqual(called_args['pool_kwargs']['server_hostname'], 'custom.hostname.com')
+        
+        # Case 2: Request without a 'Host' header (default hostname)
+        mock_request = mock.MagicMock(spec=PreparedRequest)
+        mock_request.url = "https://example.com:443/api/check"
+        mock_request.headers = {}
+        
+        adapter.get_connection_with_tls_context(mock_request, verify=True)
+        
+        # Verify that poolmanager.connection_from_host was called with the correct server_hostname
+        called_args = adapter.poolmanager.connection_from_host.call_args[1]
+        self.assertIn('pool_kwargs', called_args)
+        self.assertIn('server_hostname', called_args['pool_kwargs'])
+        self.assertEqual(called_args['pool_kwargs']['server_hostname'], 'example.com')
+        
+        # Case 3: Request with proxy and custom 'Host' header
+        mock_request = mock.MagicMock(spec=PreparedRequest)
+        mock_request.url = "https://1.2.3.4:5678/api/check"
+        mock_request.headers = {'Host': 'custom.hostname.com'}
+        
+        # Setup proxy
+        proxy = "http://127.0.0.1:8080"
+        proxies = {"https": proxy}
+        
+        # Mock the proxy manager
+        mock_proxy_manager = mock.MagicMock()
+        adapter.proxy_manager_for = mock.MagicMock(return_value=mock_proxy_manager)
+        
+        adapter.get_connection_with_tls_context(mock_request, verify=True, proxies=proxies)
+        
+        # Verify that proxy_manager.connection_from_host was called with server_hostname
+        called_args = mock_proxy_manager.connection_from_host.call_args[1]
+        self.assertIn('pool_kwargs', called_args)
+        self.assertIn('server_hostname', called_args['pool_kwargs'])
+        self.assertEqual(called_args['pool_kwargs']['server_hostname'], 'custom.hostname.com')