diff --git a/packages/pg/lib/client.js b/packages/pg/lib/client.js
index 2b13c1de7..7d0cbda31 100644
--- a/packages/pg/lib/client.js
+++ b/packages/pg/lib/client.js
@@ -438,6 +438,12 @@ class Client extends EventEmitter {
     if (activeQuery.name) {
       delete this.connection.submittedNamedStatements[activeQuery.name]
     }
+    // A paged query drives the portal with flush instead of sync, so on error
+    // the backend is still ignoring everything until a sync arrives. Send it
+    // here or ReadyForQuery never comes and the connection stays wedged.
+    if (activeQuery.rows) {
+      this.connection.sync()
+    }
     activeQuery.handleError(msg, this.connection)
   }
 
diff --git a/packages/pg/test/integration/gh-issues/3707-tests.js b/packages/pg/test/integration/gh-issues/3707-tests.js
new file mode 100644
index 000000000..f01641e9c
--- /dev/null
+++ b/packages/pg/test/integration/gh-issues/3707-tests.js
@@ -0,0 +1,27 @@
+const helper = require('../test-helper')
+const assert = require('assert')
+
+const suite = new helper.Suite()
+
+// the rows option drives the portal with flush instead of sync, which the native client does not do
+if (helper.args.native) {
+  return
+}
+
+suite.test('an error during a rows-limited query does not wedge the connection', async () => {
+  const client = new helper.pg.Client()
+  await client.connect()
+
+  await assert.rejects(
+    client.query({
+      text: 'select 10 / (5 - i) as v from generate_series(1, 7) g(i)',
+      rows: 2,
+    }),
+    /division by zero/
+  )
+
+  const { rows } = await client.query('select 1 as v')
+  assert.equal(rows[0].v, 1)
+
+  await client.end()
+})