diff --git a/spring-web/src/main/java/org/springframework/http/ReadOnlyHttpHeaders.java b/spring-web/src/main/java/org/springframework/http/ReadOnlyHttpHeaders.java
index a6e52face5..ff129f7a0c 100644
--- a/spring-web/src/main/java/org/springframework/http/ReadOnlyHttpHeaders.java
+++ b/spring-web/src/main/java/org/springframework/http/ReadOnlyHttpHeaders.java
@@ -16,9 +16,10 @@
 
 package org.springframework.http;
 
-import java.util.AbstractMap;
+import java.util.AbstractMap.SimpleImmutableEntry;
 import java.util.Collection;
 import java.util.Collections;
+import java.util.LinkedHashSet;
 import java.util.List;
 import java.util.Map;
 import java.util.Set;
@@ -31,6 +32,7 @@ import org.springframework.util.MultiValueMap;
  * {@code HttpHeaders} object that can only be read, not written to.
  *
  * @author Brian Clozel
+ * @author Sam Brannen
  * @since 5.1.1
  */
 class ReadOnlyHttpHeaders extends HttpHeaders {
@@ -141,9 +143,10 @@ class ReadOnlyHttpHeaders extends HttpHeaders {
 
 	@Override
 	public Set<Entry<String, List<String>>> entrySet() {
-		return Collections.unmodifiableSet(this.headers.entrySet().stream()
-				.map(AbstractMap.SimpleImmutableEntry::new)
-				.collect(Collectors.toSet()));
+		return this.headers.entrySet().stream().map(SimpleImmutableEntry::new)
+				.collect(Collectors.collectingAndThen(
+						Collectors.toCollection(LinkedHashSet::new), // Retain original ordering of entries
+						Collections::unmodifiableSet));
 	}
 
 }
diff --git a/spring-web/src/test/java/org/springframework/http/HttpHeadersTests.java b/spring-web/src/test/java/org/springframework/http/HttpHeadersTests.java
index 15367f54ae..a749edf9ea 100644
--- a/spring-web/src/test/java/org/springframework/http/HttpHeadersTests.java
+++ b/spring-web/src/test/java/org/springframework/http/HttpHeadersTests.java
@@ -32,6 +32,7 @@ import java.util.EnumSet;
 import java.util.GregorianCalendar;
 import java.util.List;
 import java.util.Locale;
+import java.util.Map.Entry;
 import java.util.TimeZone;
 
 import org.junit.jupiter.api.Test;
@@ -597,4 +598,20 @@ public class HttpHeadersTests {
 		assertThat(headers.get(headerName).get(0)).isEqualTo(headerValue);
 	}
 
+	@Test
+	public void readOnlyHttpHeadersRetainEntrySetOrder() {
+		headers.add("aardvark", "enigma");
+		headers.add("beaver", "enigma");
+		headers.add("cat", "enigma");
+		headers.add("dog", "enigma");
+		headers.add("elephant", "enigma");
+
+		String[] expectedKeys = new String[] { "aardvark", "beaver", "cat", "dog", "elephant" };
+
+		assertArrayEquals(expectedKeys, headers.entrySet().stream().map(Entry::getKey).toArray());
+
+		HttpHeaders readOnlyHttpHeaders = HttpHeaders.readOnlyHttpHeaders(headers);
+		assertArrayEquals(expectedKeys, readOnlyHttpHeaders.entrySet().stream().map(Entry::getKey).toArray());
+	}
+
 }