diff --git a/hugolib/page.go b/hugolib/page.go
index ec4b23d9012..537482fb269 100644
--- a/hugolib/page.go
+++ b/hugolib/page.go
@@ -360,40 +360,44 @@ func (p *pageState) setPages(pages page.Pages) {
 	p.pages = pages
 }
 
-func (p *pageState) renderResources() error {
-	var toBeDeleted []int
-
-	for i, r := range p.Resources() {
-		if _, ok := r.(page.Page); ok {
-			// Pages gets rendered with the owning page but we count them here.
-			p.s.PathSpec.ProcessingStats.Incr(&p.s.PathSpec.ProcessingStats.Pages)
-			continue
-		}
+func (p *pageState) renderResources() (err error) {
+	p.resourcesPublishInit.Do(func() {
+		var toBeDeleted []int
+
+		for i, r := range p.Resources() {
+			if _, ok := r.(page.Page); ok {
+				// Pages gets rendered with the owning page but we count them here.
+				p.s.PathSpec.ProcessingStats.Incr(&p.s.PathSpec.ProcessingStats.Pages)
+				continue
+			}
 
-		src, ok := r.(resource.Source)
-		if !ok {
-			return errors.Errorf("Resource %T does not support resource.Source", src)
-		}
+			src, ok := r.(resource.Source)
+			if !ok {
+				err = errors.Errorf("Resource %T does not support resource.Source", src)
+				return
+			}
 
-		if err := src.Publish(); err != nil {
-			if os.IsNotExist(err) {
-				// The resource has been deleted from the file system.
-				// This should be extremely rare, but can happen on live reload in server
-				// mode when the same resource is member of different page bundles.
-				toBeDeleted = append(toBeDeleted, i)
+			if err := src.Publish(); err != nil {
+				if os.IsNotExist(err) {
+					// The resource has been deleted from the file system.
+					// This should be extremely rare, but can happen on live reload in server
+					// mode when the same resource is member of different page bundles.
+					toBeDeleted = append(toBeDeleted, i)
+				} else {
+					p.s.Log.ERROR.Printf("Failed to publish Resource for page %q: %s", p.pathOrTitle(), err)
+				}
 			} else {
-				p.s.Log.ERROR.Printf("Failed to publish Resource for page %q: %s", p.pathOrTitle(), err)
+				p.s.PathSpec.ProcessingStats.Incr(&p.s.PathSpec.ProcessingStats.Files)
 			}
-		} else {
-			p.s.PathSpec.ProcessingStats.Incr(&p.s.PathSpec.ProcessingStats.Files)
 		}
-	}
 
-	for _, i := range toBeDeleted {
-		p.deleteResource(i)
-	}
+		for _, i := range toBeDeleted {
+			p.deleteResource(i)
+		}
 
-	return nil
+	})
+
+	return
 }
 
 func (p *pageState) deleteResource(i int) {
diff --git a/hugolib/page__common.go b/hugolib/page__common.go
index 5bd7223cc2d..01280bb407c 100644
--- a/hugolib/page__common.go
+++ b/hugolib/page__common.go
@@ -91,8 +91,9 @@ type pageCommon struct {
 	pagesInit sync.Once
 
 	// Any bundled resources
-	resources     resource.Resources
-	resourcesInit sync.Once
+	resources            resource.Resources
+	resourcesInit        sync.Once
+	resourcesPublishInit sync.Once
 
 	translations    page.Pages
 	allTranslations page.Pages
diff --git a/hugolib/pagebundler_test.go b/hugolib/pagebundler_test.go
index 870ea3de9a7..06bd641542f 100644
--- a/hugolib/pagebundler_test.go
+++ b/hugolib/pagebundler_test.go
@@ -896,3 +896,37 @@ TheContent.
 
 	return ps, clean, workDir
 }
+
+// https://github.com/gohugoio/hugo/issues/5858
+func TestBundledResourcesWhenMultipleOutputFormats(t *testing.T) {
+	t.Parallel()
+
+	b := newTestSitesBuilder(t).Running().WithConfigFile("toml", `
+baseURL = "https://example.org"
+[outputs]
+  # This looks odd, but it triggers the behaviour in #5858
+  # The total output formats list gets sorted, so CSS before HTML.
+  home = [ "CSS" ]
+
+`)
+	b.WithContent("mybundle/index.md", `
+---
+title: Page
+date: 2017-01-15
+---
+`,
+		"mybundle/data.json", "MyData",
+	)
+
+	b.CreateSites().Build(BuildCfg{})
+
+	b.AssertFileContent("public/mybundle/data.json", "MyData")
+
+	// Change the bundled JSON file and make sure it gets republished.
+	b.EditFiles("content/mybundle/data.json", "My changed data")
+
+	b.Build(BuildCfg{})
+
+	b.AssertFileContent("public/mybundle/data.json", "My changed data")
+
+}
diff --git a/hugolib/shortcode_test.go b/hugolib/shortcode_test.go
index 3320e642c44..dd01eb5c504 100644
--- a/hugolib/shortcode_test.go
+++ b/hugolib/shortcode_test.go
@@ -903,6 +903,7 @@ func TestShortcodeParentResourcesOnRebuild(t *testing.T) {
 	b.WithTemplatesAdded(
 		"index.html", `
 {{ $b := .Site.GetPage "b1" }}
+b1 Content: {{ $b.Content }}
 {{$p := $b.Resources.GetMatch "p1*" }}
 Content: {{ $p.Content }}
 {{ $article := .Site.GetPage "blog/article" }}
@@ -933,20 +934,23 @@ SHORTCODE: {{< c >}}
 
 	b.Build(BuildCfg{})
 
-	assert := func() {
-		b.AssertFileContent("public/index.html",
-			"Parent resource: logo.png: /b1/logo.png",
+	assert := func(matchers ...string) {
+		allMatchers := append(matchers, "Parent resource: logo.png: /b1/logo.png",
 			"Article Content: <p>SHORTCODE: \n\n* Parent resource: logo-article.png: /blog/logo-article.png",
 		)
+
+		b.AssertFileContent("public/index.html",
+			allMatchers...,
+		)
 	}
 
 	assert()
 
-	b.EditFiles("b1/index.md", pageContent+" Edit.")
+	b.EditFiles("content/b1/index.md", pageContent+" Edit.")
 
 	b.Build(BuildCfg{})
 
-	assert()
+	assert("Edit.")
 
 }
 
diff --git a/hugolib/site_render.go b/hugolib/site_render.go
index 407061b6778..9ade951df1a 100644
--- a/hugolib/site_render.go
+++ b/hugolib/site_render.go
@@ -35,6 +35,7 @@ type siteRenderContext struct {
 	sitesOutIdx int
 
 	// Zero based index of the output formats configured within a Site.
+	// Note that these outputs are sorted, so CSS will come before HTML.
 	outIdx int
 
 	multihost bool
@@ -130,11 +131,9 @@ func pageRenderer(
 			continue
 		}
 
-		if ctx.outIdx == 0 {
-			if err := p.renderResources(); err != nil {
-				s.SendError(p.errorf(err, "failed to render page resources"))
-				continue
-			}
+		if err := p.renderResources(); err != nil {
+			s.SendError(p.errorf(err, "failed to render page resources"))
+			continue
 		}
 
 		layouts, err := p.getLayouts()