diff --git a/haystack/core/pipeline/pipeline.py b/haystack/core/pipeline/pipeline.py
index 5737d3095..10d0389a3 100644
--- a/haystack/core/pipeline/pipeline.py
+++ b/haystack/core/pipeline/pipeline.py
@@ -948,6 +948,26 @@ class Pipeline:
                             if not there_are_only_lazy_variadics:
                                 continue
 
+                        # Components that have defaults for all their inputs must be treated the same identical way as we treat
+                        # lazy variadic components. If there are only components with defaults we can run them.
+                        # If we don't do this the order of execution of the Pipeline's Components will be affected cause we
+                        # enqueue the Components in `to_run` at the start using the order they are added in the Pipeline.
+                        # If a Component A with defaults is added before a Component B that has no defaults, but in the Pipeline
+                        # logic A must be executed after B it could run instead before if we don't do this check.
+                        has_only_defaults = all(
+                            not socket.is_mandatory for socket in comp.__haystack_input__._sockets_dict.values()  # type: ignore
+                        )
+                        if has_only_defaults:
+                            there_are_only_components_with_defaults = True
+                            for other_name, other_comp in waiting_for_input:
+                                if name == other_name:
+                                    continue
+                                there_are_only_components_with_defaults &= all(
+                                    not s.is_mandatory for s in other_comp.__haystack_input__._sockets_dict.values()  # type: ignore
+                                )
+                            if not there_are_only_components_with_defaults:
+                                continue
+
                         # Find the first component that has all the inputs it needs to run
                         has_enough_inputs = True
                         for input_socket in comp.__haystack_input__._sockets_dict.values():  # type: ignore
diff --git a/releasenotes/notes/fix-pipeline-run-disorder-382da1e6bd6db510.yaml b/releasenotes/notes/fix-pipeline-run-disorder-382da1e6bd6db510.yaml
new file mode 100644
index 000000000..e5255e603
--- /dev/null
+++ b/releasenotes/notes/fix-pipeline-run-disorder-382da1e6bd6db510.yaml
@@ -0,0 +1,7 @@
+---
+fixes:
+  - |
+    Fixes `Pipeline.run()` logic so Components that have all their inputs with a default are run in the correct order.
+    This happened we gather a list of Components to run internally when running the Pipeline in the order they are
+    added during creation of the Pipeline.
+    This caused some Components to run before they received all their inputs.
diff --git a/test/core/pipeline/test_pipeline.py b/test/core/pipeline/test_pipeline.py
index ef15ccf1a..ab493b9c6 100644
--- a/test/core/pipeline/test_pipeline.py
+++ b/test/core/pipeline/test_pipeline.py
@@ -756,3 +756,54 @@ def test_walk_pipeline_with_cycles():
     pipeline.add_component("hello", hello)
     pipeline.connect("hello.intermediate", "hello.intermediate")
     assert [("hello", hello)] == list(pipeline.walk())
+
+
+def test_correct_execution_order_of_components_with_only_defaults(spying_tracer):
+    """
+    We enqueue the Components in internal `to_run` data structure at the start of `Pipeline.run()` using the order
+    they are added in the Pipeline with `Pipeline.add_component()`.
+    If a Component A with defaults is added before a Component B that has no defaults, but in the Pipeline
+    logic A must be executed after B it could run instead before.
+
+    This test verifies that the order of execution is correct.
+    """
+    docs = [Document(content="Rome is the capital of Italy"), Document(content="Paris is the capital of France")]
+    doc_store = InMemoryDocumentStore()
+    doc_store.write_documents(docs)
+    template = (
+        "Given the following information, answer the question.\n"
+        "Context:\n"
+        "{% for document in documents %}"
+        "    {{ document.content }}\n"
+        "{% endfor %}"
+        "Question: {{ query }}"
+    )
+
+    pipe = Pipeline()
+
+    # The order of this addition is important for the test
+    # Do not edit them.
+    pipe.add_component("prompt_builder", PromptBuilder(template=template))
+    pipe.add_component("retriever", InMemoryBM25Retriever(document_store=doc_store))
+    pipe.connect("retriever", "prompt_builder.documents")
+
+    query = "What is the capital of France?"
+    res = pipe.run({"prompt_builder": {"query": query}, "retriever": {"query": query}})
+
+    assert len(spying_tracer.spans) == 3
+    assert spying_tracer.spans[0].operation_name == "haystack.pipeline.run"
+    assert spying_tracer.spans[1].operation_name == "haystack.component.run"
+    assert spying_tracer.spans[1].tags["haystack.component.name"] == "retriever"
+    assert spying_tracer.spans[2].operation_name == "haystack.component.run"
+    assert spying_tracer.spans[2].tags["haystack.component.name"] == "prompt_builder"
+
+    print(res["prompt_builder"]["prompt"])
+    assert res == {
+        "prompt_builder": {
+            "prompt": "Given the following information, answer the question.\n"
+            "Context:\n"
+            "    Paris is the capital of France\n"
+            "    Rome is the capital of Italy\n"
+            "Question: What is the capital of France?"
+        }
+    }