diff --git a/rules/group.go b/rules/group.go
index 9ad9aab093..a83c33a8e8 100644
--- a/rules/group.go
+++ b/rules/group.go
@@ -1110,9 +1110,6 @@ func buildDependencyMap(rules []Rule) dependencyMap {
 		return dependencies
 	}
 
-	inputs := make(map[string][]Rule, len(rules))
-	outputs := make(map[string][]Rule, len(rules))
-
 	var indeterminate bool
 
 	for _, rule := range rules {
@@ -1120,26 +1117,46 @@ func buildDependencyMap(rules []Rule) dependencyMap {
 			break
 		}
 
-		name := rule.Name()
-		outputs[name] = append(outputs[name], rule)
-
 		parser.Inspect(rule.Query(), func(node parser.Node, path []parser.Node) error {
 			if n, ok := node.(*parser.VectorSelector); ok {
+				// Find the name matcher for the rule.
+				var nameMatcher *labels.Matcher
+				if n.Name != "" {
+					nameMatcher = labels.MustNewMatcher(labels.MatchEqual, model.MetricNameLabel, n.Name)
+				} else {
+					for _, m := range n.LabelMatchers {
+						if m.Name == model.MetricNameLabel {
+							nameMatcher = m
+							break
+						}
+					}
+				}
+
 				// A wildcard metric expression means we cannot reliably determine if this rule depends on any other,
 				// which means we cannot safely run any rules concurrently.
-				if n.Name == "" && len(n.LabelMatchers) > 0 {
+				if nameMatcher == nil {
 					indeterminate = true
 					return nil
 				}
 
 				// Rules which depend on "meta-metrics" like ALERTS and ALERTS_FOR_STATE will have undefined behaviour
 				// if they run concurrently.
-				if n.Name == alertMetricName || n.Name == alertForStateMetricName {
+				if nameMatcher.Matches(alertMetricName) || nameMatcher.Matches(alertForStateMetricName) {
 					indeterminate = true
 					return nil
 				}
 
-				inputs[n.Name] = append(inputs[n.Name], rule)
+				// Find rules which depend on the output of this rule.
+				for _, other := range rules {
+					if other == rule {
+						continue
+					}
+
+					otherName := other.Name()
+					if nameMatcher.Matches(otherName) {
+						dependencies[other] = append(dependencies[other], rule)
+					}
+				}
 			}
 			return nil
 		})
@@ -1149,13 +1166,5 @@ func buildDependencyMap(rules []Rule) dependencyMap {
 		return nil
 	}
 
-	for output, outRules := range outputs {
-		for _, outRule := range outRules {
-			if inRules, found := inputs[output]; found && len(inRules) > 0 {
-				dependencies[outRule] = append(dependencies[outRule], inRules...)
-			}
-		}
-	}
-
 	return dependencies
 }
diff --git a/rules/manager_test.go b/rules/manager_test.go
index 6c32b6d0f1..9ef1fcf074 100644
--- a/rules/manager_test.go
+++ b/rules/manager_test.go
@@ -1601,10 +1601,14 @@ func TestDependencyMap(t *testing.T) {
 	require.NoError(t, err)
 	rule4 := NewRecordingRule("user:requests:increase1h", expr, labels.Labels{})
 
+	expr, err = parser.ParseExpr(`sum by (user) ({__name__=~"user:requests.+5m"})`)
+	require.NoError(t, err)
+	rule5 := NewRecordingRule("user:requests:sum5m", expr, labels.Labels{})
+
 	group := NewGroup(GroupOptions{
 		Name:     "rule_group",
 		Interval: time.Second,
-		Rules:    []Rule{rule, rule2, rule3, rule4},
+		Rules:    []Rule{rule, rule2, rule3, rule4, rule5},
 		Opts:     opts,
 	})
 
@@ -1619,13 +1623,17 @@ func TestDependencyMap(t *testing.T) {
 	require.Equal(t, []Rule{rule}, depMap.dependencies(rule2))
 	require.False(t, depMap.isIndependent(rule2))
 
-	require.Zero(t, depMap.dependents(rule3))
+	require.Equal(t, []Rule{rule5}, depMap.dependents(rule3))
 	require.Zero(t, depMap.dependencies(rule3))
-	require.True(t, depMap.isIndependent(rule3))
+	require.False(t, depMap.isIndependent(rule3))
 
 	require.Zero(t, depMap.dependents(rule4))
 	require.Equal(t, []Rule{rule}, depMap.dependencies(rule4))
 	require.False(t, depMap.isIndependent(rule4))
+
+	require.Zero(t, depMap.dependents(rule5))
+	require.Equal(t, []Rule{rule3}, depMap.dependencies(rule5))
+	require.False(t, depMap.isIndependent(rule5))
 }
 
 func TestNoDependency(t *testing.T) {