diff --git a/lib/internal/http2/core.js b/lib/internal/http2/core.js
index 1b010fbe6b3a89..a8285fd9d95692 100755
--- a/lib/internal/http2/core.js
+++ b/lib/internal/http2/core.js
@@ -462,7 +462,7 @@ function requestOnConnect(headers, options) {
       break;
     case NGHTTP2_ERR_STREAM_ID_NOT_AVAILABLE:
       err = new errors.Error('ERR_HTTP2_OUT_OF_STREAMS');
-      process.nextTick(() => this.emit('error', err));
+      process.nextTick(() => session.emit('error', err));
       break;
     case NGHTTP2_ERR_INVALID_ARGUMENT:
       err = new errors.Error('ERR_HTTP2_STREAM_SELF_DEPENDENCY');
diff --git a/test/parallel/test-http2-client-onconnect-errors.js b/test/parallel/test-http2-client-onconnect-errors.js
new file mode 100644
index 00000000000000..2e9f946194b05a
--- /dev/null
+++ b/test/parallel/test-http2-client-onconnect-errors.js
@@ -0,0 +1,124 @@
+// Flags: --expose-http2
+'use strict';
+
+const {
+  constants,
+  Http2Session,
+  nghttp2ErrorString
+} = process.binding('http2');
+const common = require('../common');
+if (!common.hasCrypto)
+  common.skip('missing crypto');
+const http2 = require('http2');
+
+// tests error handling within requestOnConnect
+// - NGHTTP2_ERR_NOMEM (should emit session error)
+// - NGHTTP2_ERR_STREAM_ID_NOT_AVAILABLE (should emit session error)
+// - NGHTTP2_ERR_INVALID_ARGUMENT (should emit stream error)
+// - every other NGHTTP2 error from binding (should emit session error)
+
+const specificTestKeys = [
+  'NGHTTP2_ERR_NOMEM',
+  'NGHTTP2_ERR_STREAM_ID_NOT_AVAILABLE',
+  'NGHTTP2_ERR_INVALID_ARGUMENT'
+];
+
+const specificTests = [
+  {
+    ngError: constants.NGHTTP2_ERR_NOMEM,
+    error: {
+      code: 'ERR_OUTOFMEMORY',
+      type: Error,
+      message: 'Out of memory'
+    },
+    type: 'session'
+  },
+  {
+    ngError: constants.NGHTTP2_ERR_STREAM_ID_NOT_AVAILABLE,
+    error: {
+      code: 'ERR_HTTP2_OUT_OF_STREAMS',
+      type: Error,
+      message: 'No stream ID is available because ' +
+               'maximum stream ID has been reached'
+    },
+    type: 'session'
+  },
+  {
+    ngError: constants.NGHTTP2_ERR_INVALID_ARGUMENT,
+    error: {
+      code: 'ERR_HTTP2_STREAM_SELF_DEPENDENCY',
+      type: Error,
+      message: 'A stream cannot depend on itself'
+    },
+    type: 'stream'
+  },
+];
+
+const genericTests = Object.getOwnPropertyNames(constants)
+  .filter((key) => (
+    key.indexOf('NGHTTP2_ERR') === 0 && specificTestKeys.indexOf(key) < 0
+  ))
+  .map((key) => ({
+    ngError: constants[key],
+    error: {
+      code: 'ERR_HTTP2_ERROR',
+      type: Error,
+      message: nghttp2ErrorString(constants[key])
+    },
+    type: 'session'
+  }));
+
+const tests = specificTests.concat(genericTests);
+
+let currentError;
+
+// mock submitRequest because we only care about testing error handling
+Http2Session.prototype.submitRequest = () => currentError;
+
+const server = http2.createServer(common.mustNotCall());
+
+server.listen(0, common.mustCall(() => runTest(tests.shift())));
+
+function runTest(test) {
+  const port = server.address().port;
+  const url = `http://localhost:${port}`;
+  const headers = {
+    ':path': '/',
+    ':method': 'POST',
+    ':scheme': 'http',
+    ':authority': `localhost:${port}`
+  };
+
+  const client = http2.connect(url);
+  const req = client.request(headers);
+
+  currentError = test.ngError;
+  req.resume();
+  req.end();
+
+  const errorMustCall = common.expectsError(test.error);
+  const errorMustNotCall = common.mustNotCall(
+    `${test.error.code} should emit on ${test.type}`
+  );
+
+  if (test.type === 'stream') {
+    client.on('error', errorMustNotCall);
+    req.on('error', errorMustCall);
+    req.on('error', common.mustCall(() => {
+      client.destroy();
+    }));
+  } else {
+    client.on('error', errorMustCall);
+    req.on('error', errorMustNotCall);
+  }
+
+  req.on('end', common.mustCall(() => {
+    client.destroy();
+
+    if (!tests.length) {
+      server.close();
+    } else {
+      runTest(tests.shift());
+    }
+  }));
+}