HelpersPlugin.php

<? namespace Craft;

class HelpersPlugin extends BasePlugin
{
  public function getName()
  {
    return Craft::t('Helpers');
  }

  public function getVersion()
  {
    return '1.0';
  }

  public function getDeveloper()
  {
    return 'oof. Studio';
  }

  public function getDeveloperUrl()
  {
    return 'http://oof.studio/';
  }

  public function hasCpSection()
  {
    return false;
  }

  public function addTwigExtension()
  {
    Craft::import('plugins.helpers.twigextensions.HelpersTwigExtension');
    return new HelpersTwigExtension();
  }
}

HelpersTwigExtension.php

<?php namespace Craft;

class HelpersTwigExtension extends \Twig_Extension
{
  public function getName()
  {
    return 'Helpers Twig Extension';
  }

  public function getFilters()
  {
    $filters = [];
    $methods = [
      'mdline' => 'markdownSingleLine'
    ];

    foreach ($methods as $key => $method) {
      $filters[$key] = new \Twig_Filter_Method($this, $method);
    }

    return $filters;
  }

  /*
   * Twig proxy for Craft's built-in single-line markdown parsing function
   */
  public function markdownSingleLine($md)
  {
    return StringHelper::parseMarkdownLine($md);
  }
}

template.twig

Standard markdown still works:
{{ entry.markdownField | md }} {# or `markdown` #}

This adds the following filter, which strips out block-level tags:
{{ entry.markdownField | mdline }}

Plugin structure should look like this:

helpers/
  - HelpersPlugin.php
  - twigextensions/
    - HelpersTwigExtension.php