diff --git a/sql/core/src/main/scala/org/apache/spark/sql/execution/datasources/DataSourceUtils.scala b/sql/core/src/main/scala/org/apache/spark/sql/execution/datasources/DataSourceUtils.scala
index f8068a634977b..b54747a25d5a3 100644
--- a/sql/core/src/main/scala/org/apache/spark/sql/execution/datasources/DataSourceUtils.scala
+++ b/sql/core/src/main/scala/org/apache/spark/sql/execution/datasources/DataSourceUtils.scala
@@ -26,7 +26,7 @@ import org.json4s.NoTypeHints
 import org.json4s.jackson.Serialization
 
 import org.apache.spark.SparkUpgradeException
-import org.apache.spark.sql.{SPARK_INT96_NO_REBASE, SPARK_LEGACY_DATETIME, SPARK_VERSION_METADATA_KEY}
+import org.apache.spark.sql.{SPARK_LEGACY_DATETIME, SPARK_LEGACY_INT96, SPARK_VERSION_METADATA_KEY}
 import org.apache.spark.sql.AnalysisException
 import org.apache.spark.sql.catalyst.catalog.{CatalogTable, CatalogUtils}
 import org.apache.spark.sql.catalyst.util.RebaseDateTime
@@ -115,14 +115,20 @@ object DataSourceUtils {
       lookupFileMeta: String => String,
       modeByConfig: String): LegacyBehaviorPolicy.Value = {
     if (Utils.isTesting && SQLConf.get.getConfString("spark.test.forceNoRebase", "") == "true") {
-      LegacyBehaviorPolicy.CORRECTED
-    } else if (lookupFileMeta(SPARK_INT96_NO_REBASE) != null) {
-      LegacyBehaviorPolicy.CORRECTED
-    } else if (lookupFileMeta(SPARK_VERSION_METADATA_KEY) != null) {
-      LegacyBehaviorPolicy.LEGACY
-    } else {
-      LegacyBehaviorPolicy.withName(modeByConfig)
+      return LegacyBehaviorPolicy.CORRECTED
     }
+    // If there is no version, we return the mode specified by the config.
+    Option(lookupFileMeta(SPARK_VERSION_METADATA_KEY)).map { version =>
+      // Files written by Spark 3.0 and earlier follow the legacy hybrid calendar and we need to
+      // rebase the INT96 timestamp values.
+      // Files written by Spark 3.1 and latter may also need the rebase if they were written with
+      // the "LEGACY" rebase mode.
+      if (version < "3.1.0" || lookupFileMeta(SPARK_LEGACY_INT96) != null) {
+        LegacyBehaviorPolicy.LEGACY
+      } else {
+        LegacyBehaviorPolicy.CORRECTED
+      }
+    }.getOrElse(LegacyBehaviorPolicy.withName(modeByConfig))
   }
 
   def newRebaseExceptionInRead(format: String): SparkUpgradeException = {
diff --git a/sql/core/src/main/scala/org/apache/spark/sql/execution/datasources/parquet/ParquetWriteSupport.scala b/sql/core/src/main/scala/org/apache/spark/sql/execution/datasources/parquet/ParquetWriteSupport.scala
index b538c2f2493d0..26074719364a4 100644
--- a/sql/core/src/main/scala/org/apache/spark/sql/execution/datasources/parquet/ParquetWriteSupport.scala
+++ b/sql/core/src/main/scala/org/apache/spark/sql/execution/datasources/parquet/ParquetWriteSupport.scala
@@ -31,7 +31,7 @@ import org.apache.parquet.io.api.{Binary, RecordConsumer}
 
 import org.apache.spark.SPARK_VERSION_SHORT
 import org.apache.spark.internal.Logging
-import org.apache.spark.sql.{SPARK_INT96_NO_REBASE, SPARK_LEGACY_DATETIME, SPARK_VERSION_METADATA_KEY}
+import org.apache.spark.sql.{SPARK_LEGACY_DATETIME, SPARK_LEGACY_INT96, SPARK_VERSION_METADATA_KEY}
 import org.apache.spark.sql.catalyst.InternalRow
 import org.apache.spark.sql.catalyst.expressions.SpecializedGetters
 import org.apache.spark.sql.catalyst.util.DateTimeUtils
@@ -123,9 +123,9 @@ class ParquetWriteSupport extends WriteSupport[InternalRow] with Logging {
       }
     } ++ {
       if (int96RebaseMode == LegacyBehaviorPolicy.LEGACY) {
-        None
+        Some(SPARK_LEGACY_INT96 -> "")
       } else {
-        Some(SPARK_INT96_NO_REBASE -> "")
+        None
       }
     }
 
diff --git a/sql/core/src/main/scala/org/apache/spark/sql/package.scala b/sql/core/src/main/scala/org/apache/spark/sql/package.scala
index 011be6d69c576..022fecf1ae412 100644
--- a/sql/core/src/main/scala/org/apache/spark/sql/package.scala
+++ b/sql/core/src/main/scala/org/apache/spark/sql/package.scala
@@ -63,7 +63,7 @@ package object sql {
 
   /**
    * Parquet file metadata key to indicate that the file with INT96 column type was written
-   * without rebasing.
+   * with rebasing.
    */
-  private[sql] val SPARK_INT96_NO_REBASE = "org.apache.spark.int96NoRebase"
+  private[sql] val SPARK_LEGACY_INT96 = "org.apache.spark.legacyINT96"
 }
diff --git a/sql/core/src/test/scala/org/apache/spark/sql/execution/datasources/parquet/ParquetIOSuite.scala b/sql/core/src/test/scala/org/apache/spark/sql/execution/datasources/parquet/ParquetIOSuite.scala
index dac4e950a7823..34bdef7bdb402 100644
--- a/sql/core/src/test/scala/org/apache/spark/sql/execution/datasources/parquet/ParquetIOSuite.scala
+++ b/sql/core/src/test/scala/org/apache/spark/sql/execution/datasources/parquet/ParquetIOSuite.scala
@@ -1163,9 +1163,9 @@ class ParquetIOSuite extends QueryTest with ParquetTest with SharedSparkSession
     }
   }
 
-  test("SPARK-33160: write the metadata key 'org.apache.spark.int96NoRebase'") {
-    def saveTs(dir: java.io.File): Unit = {
-      Seq(Timestamp.valueOf("1000-01-01 01:02:03")).toDF()
+  test("SPARK-33160: write the metadata key 'org.apache.spark.legacyINT96'") {
+    def saveTs(dir: java.io.File, ts: String = "1000-01-01 01:02:03"): Unit = {
+      Seq(Timestamp.valueOf(ts)).toDF()
         .repartition(1)
         .write
         .parquet(dir.getAbsolutePath)
@@ -1173,18 +1173,24 @@ class ParquetIOSuite extends QueryTest with ParquetTest with SharedSparkSession
     withSQLConf(SQLConf.LEGACY_PARQUET_INT96_REBASE_MODE_IN_WRITE.key -> LEGACY.toString) {
       withTempPath { dir =>
         saveTs(dir)
-        assert(getMetaData(dir).get(SPARK_INT96_NO_REBASE).isEmpty)
+        assert(getMetaData(dir)(SPARK_LEGACY_INT96) === "")
       }
     }
     withSQLConf(SQLConf.LEGACY_PARQUET_INT96_REBASE_MODE_IN_WRITE.key -> CORRECTED.toString) {
       withTempPath { dir =>
         saveTs(dir)
-        assert(getMetaData(dir)(SPARK_INT96_NO_REBASE) === "")
+        assert(getMetaData(dir).get(SPARK_LEGACY_INT96).isEmpty)
       }
     }
     withSQLConf(SQLConf.LEGACY_PARQUET_INT96_REBASE_MODE_IN_WRITE.key -> EXCEPTION.toString) {
       withTempPath { dir => intercept[SparkException] { saveTs(dir) } }
     }
+    withSQLConf(SQLConf.LEGACY_PARQUET_INT96_REBASE_MODE_IN_WRITE.key -> EXCEPTION.toString) {
+      withTempPath { dir =>
+        saveTs(dir, "2020-10-22 01:02:03")
+        assert(getMetaData(dir).get(SPARK_LEGACY_INT96).isEmpty)
+      }
+    }
   }
 }
 
diff --git a/sql/hive/src/test/scala/org/apache/spark/sql/hive/StatisticsSuite.scala b/sql/hive/src/test/scala/org/apache/spark/sql/hive/StatisticsSuite.scala
index db0e93787338e..7d5a200606356 100644
--- a/sql/hive/src/test/scala/org/apache/spark/sql/hive/StatisticsSuite.scala
+++ b/sql/hive/src/test/scala/org/apache/spark/sql/hive/StatisticsSuite.scala
@@ -1513,7 +1513,7 @@ class StatisticsSuite extends StatisticsCollectionTestBase with TestHiveSingleto
         Seq(tbl, ext_tbl).foreach { tblName =>
           sql(s"INSERT INTO $tblName VALUES (1, 'a', '2019-12-13')")
 
-          val expectedSize = 636
+          val expectedSize = 601
           // analyze table
           sql(s"ANALYZE TABLE $tblName COMPUTE STATISTICS NOSCAN")
           var tableStats = getTableStats(tblName)