diff --git a/src/cmd/go/internal/load/pkg.go b/src/cmd/go/internal/load/pkg.go
index 98a695ca24a..79c3a71f074 100644
--- a/src/cmd/go/internal/load/pkg.go
+++ b/src/cmd/go/internal/load/pkg.go
@@ -480,6 +480,7 @@ type ImportPathError interface {
 
 var (
 	_ ImportPathError = (*importError)(nil)
+	_ ImportPathError = (*mainPackageError)(nil)
 	_ ImportPathError = (*modload.ImportMissingError)(nil)
 	_ ImportPathError = (*modload.ImportMissingSumError)(nil)
 	_ ImportPathError = (*modload.DirectImportFromImplicitDependencyError)(nil)
@@ -2545,7 +2546,8 @@ func CheckPackageErrors(pkgs []*Package) {
 // mainPackagesOnly filters out non-main packages matched only by arguments
 // containing "..." and returns the remaining main packages.
 //
-// mainPackagesOnly sets a package's error if it is named by a literal argument.
+// mainPackagesOnly sets a non-main package's Error field and returns it if it
+// is named by a literal argument.
 //
 // mainPackagesOnly prints warnings for non-literal arguments that only match
 // non-main packages.
@@ -2557,12 +2559,12 @@ func mainPackagesOnly(pkgs []*Package, patterns []string) []*Package {
 		}
 	}
 
-	mainPkgs := make([]*Package, 0, len(pkgs))
+	matchedPkgs := make([]*Package, 0, len(pkgs))
 	mainCount := make([]int, len(patterns))
 	nonMainCount := make([]int, len(patterns))
 	for _, pkg := range pkgs {
 		if pkg.Name == "main" {
-			mainPkgs = append(mainPkgs, pkg)
+			matchedPkgs = append(matchedPkgs, pkg)
 			for i := range patterns {
 				if matchers[i] != nil && matchers[i](pkg.ImportPath) {
 					mainCount[i]++
@@ -2570,8 +2572,11 @@ func mainPackagesOnly(pkgs []*Package, patterns []string) []*Package {
 			}
 		} else {
 			for i := range patterns {
-				if matchers[i] == nil && patterns[i] == pkg.ImportPath && pkg.Error == nil {
-					pkg.Error = &PackageError{Err: ImportErrorf(pkg.ImportPath, "package %s is not a main package", pkg.ImportPath)}
+				if matchers[i] == nil && patterns[i] == pkg.ImportPath {
+					if pkg.Error == nil {
+						pkg.Error = &PackageError{Err: &mainPackageError{importPath: pkg.ImportPath}}
+					}
+					matchedPkgs = append(matchedPkgs, pkg)
 				} else if matchers[i] != nil && matchers[i](pkg.ImportPath) {
 					nonMainCount[i]++
 				}
@@ -2584,7 +2589,19 @@ func mainPackagesOnly(pkgs []*Package, patterns []string) []*Package {
 		}
 	}
 
-	return mainPkgs
+	return matchedPkgs
+}
+
+type mainPackageError struct {
+	importPath string
+}
+
+func (e *mainPackageError) Error() string {
+	return fmt.Sprintf("package %s is not a main package", e.importPath)
+}
+
+func (e *mainPackageError) ImportPath() string {
+	return e.importPath
 }
 
 func setToolFlags(pkgs ...*Package) {
@@ -2679,6 +2696,9 @@ func GoFilesPackage(ctx context.Context, opts PackageOpts, gofiles []string) *Pa
 		}
 	}
 
+	if opts.MainOnly && pkg.Name != "main" && pkg.Error == nil {
+		pkg.Error = &PackageError{Err: &mainPackageError{importPath: pkg.ImportPath}}
+	}
 	setToolFlags(pkg)
 
 	return pkg
diff --git a/src/cmd/go/internal/run/run.go b/src/cmd/go/internal/run/run.go
index 914e5edc6f2..784f7162dfd 100644
--- a/src/cmd/go/internal/run/run.go
+++ b/src/cmd/go/internal/run/run.go
@@ -92,6 +92,7 @@ func runRun(ctx context.Context, cmd *base.Command, args []string) {
 	for i < len(args) && strings.HasSuffix(args[i], ".go") {
 		i++
 	}
+	pkgOpts := load.PackageOpts{MainOnly: true}
 	var p *load.Package
 	if i > 0 {
 		files := args[:i]
@@ -102,10 +103,9 @@ func runRun(ctx context.Context, cmd *base.Command, args []string) {
 				base.Fatalf("go run: cannot run *_test.go files (%s)", file)
 			}
 		}
-		p = load.GoFilesPackage(ctx, load.PackageOpts{}, files)
+		p = load.GoFilesPackage(ctx, pkgOpts, files)
 	} else if len(args) > 0 && !strings.HasPrefix(args[0], "-") {
 		arg := args[0]
-		pkgOpts := load.PackageOpts{MainOnly: true}
 		var pkgs []*load.Package
 		if strings.Contains(arg, "@") && !build.IsLocalImport(arg) && !filepath.IsAbs(arg) {
 			var err error
@@ -133,9 +133,6 @@ func runRun(ctx context.Context, cmd *base.Command, args []string) {
 		base.Fatalf("go run: no go files listed")
 	}
 	cmdArgs := args[i:]
-	if p.Name != "main" {
-		base.Fatalf("go run: cannot run non-main package")
-	}
 	load.CheckPackageErrors([]*load.Package{p})
 
 	p.Internal.OmitDebug = true
diff --git a/src/cmd/go/testdata/script/mod_install_pkg_version.txt b/src/cmd/go/testdata/script/mod_install_pkg_version.txt
index 3b387cd8b69..9a803c4218a 100644
--- a/src/cmd/go/testdata/script/mod_install_pkg_version.txt
+++ b/src/cmd/go/testdata/script/mod_install_pkg_version.txt
@@ -118,7 +118,7 @@ stderr '^package rsc.io/fortune provided by module rsc.io/fortune@v1.0.0\n\tAll
 # 'go install pkg@version' should report an error if an argument is not
 # a main package.
 ! go install example.com/cmd/a@v1.0.0 example.com/cmd/err@v1.0.0
-stderr '^go: package example.com/cmd/err is not a main package$'
+stderr '^package example.com/cmd/err is not a main package$'
 
 # Wildcards should match only main packages. This module has a non-main package
 # with an error, so we'll know if that gets built.
diff --git a/src/cmd/go/testdata/script/mod_outside.txt b/src/cmd/go/testdata/script/mod_outside.txt
index 0b01492cde1..33341f7d4b3 100644
--- a/src/cmd/go/testdata/script/mod_outside.txt
+++ b/src/cmd/go/testdata/script/mod_outside.txt
@@ -207,10 +207,6 @@ stderr 'needmod[/\\]needmod.go:10:2: no required module provides package example
 go install cmd/addr2line
 ! stderr .
 
-# 'go run' with a version should fail due to syntax.
-! go run example.com/printversion@v1.0.0
-stderr 'can only use path@version syntax with'
-
 # 'go run' should fail if a package argument must be resolved to a module.
 ! go run example.com/printversion
 stderr '^no required module provides package example.com/printversion: go.mod file not found in current directory or any parent directory; see ''go help modules''$'
diff --git a/src/cmd/go/testdata/script/mod_run_pkg_version.txt b/src/cmd/go/testdata/script/mod_run_pkg_version.txt
index d96d3fc2133..48462230b65 100644
--- a/src/cmd/go/testdata/script/mod_run_pkg_version.txt
+++ b/src/cmd/go/testdata/script/mod_run_pkg_version.txt
@@ -36,6 +36,11 @@ stderr '^go: found rsc.io/quote in rsc.io/quote v1.5.2$'
 stderr '^Hello, world.$'
 
 
+# 'go run pkg@version' should report an error if pkg is not a main package.
+! go run example.com/cmd/err@v1.0.0
+stderr '^package example.com/cmd/err is not a main package$'
+
+
 # 'go run pkg@version' should report errors if the module contains
 # replace or exclude directives.
 go mod download example.com/cmd@v1.0.0-replace