diff --git a/parse.go b/parse.go
index e31dc839..33d8f025 100644
--- a/parse.go
+++ b/parse.go
@@ -372,6 +372,9 @@ func (p *parser) valueDatetime(it item) (any, tomlType) {
 		}
 		t, err = time.ParseInLocation(dt.fmt, it.val, dt.zone)
 		if err == nil {
+			if missingLeadingZero(it.val, dt.fmt) {
+				p.panicErr(it, errParseDate{it.val})
+			}
 			ok = true
 			break
 		}
@@ -382,6 +385,23 @@ func (p *parser) valueDatetime(it item) (any, tomlType) {
 	return t, p.typeOfPrimitive(it)
 }
 
+// Go's time.Parse() will accept numbers without a leading zero; there isn't any
+// way to require it. https://github.com/golang/go/issues/29911
+//
+// Depend on the fact that the separators (- and :) should always be at the same
+// location.
+func missingLeadingZero(d, l string) bool {
+	for i, c := range []byte(l) {
+		if c == '.' || c == 'Z' {
+			return false
+		}
+		if (c < '0' || c > '9') && d[i] != c {
+			return true
+		}
+	}
+	return false
+}
+
 func (p *parser) valueArray(it item) (any, tomlType) {
 	p.setType(p.currentKey, tomlArray, it.pos)
 
diff --git a/toml_test.go b/toml_test.go
index 8f650e22..920f96dc 100644
--- a/toml_test.go
+++ b/toml_test.go
@@ -304,15 +304,6 @@ func runTomlTest(t *testing.T, includeNext bool, wantFail ...string) {
 			Parser:   parser{},
 			RunTests: runTests,
 			SkipTests: []string{
-				// "15" in time.Parse() accepts both "1" and "01". The TOML
-				// specification says that times *must* start with a leading
-				// zero, but this requires writing out own datetime parser.
-				// I think it's actually okay to just accept both really.
-				// https://github.com/BurntSushi/toml/issues/320
-				"invalid/datetime/time-no-leads",
-				"invalid/local-time/time-no-leads",
-				"invalid/local-datetime/time-no-leads",
-
 				// These tests are fine, just doesn't deal well with empty output.
 				"valid/comment/noeol",
 				"valid/comment/nonascii",