An Andre Gray double had put the Bees firmly in the driving seat before the Lions roared back at the New Den to level the score.
Shittu got the first of those to inspire a fightback and Alan Dunne netted a minute later in a crazy few seconds for Mark Warburton’s men.
But he went from hero to zero just as quickly to hand Brentford their third straight win and propel them into the top six.
Bees boss Warburton said: “We perhaps lacked a bit of self belief at the start of the season and questioned whether we can handle it at this level, but we have now shown that we can."