Rookie Bees' defender Leon Legge kept free scoring Leeds' striker Jermaine Beckford quiet for most of the game, restricting him to just one clear-cut chance.
The forward raced through on goal but his cool side-foot was tipped wide by home keeper Wokciech Szczesny.
Beckford's strike partner Luciano Becchio almost broke the deadlock just after the break when his dipping volley skimmed off the bar.
But Brentford had their chances, with Sam Saunders seeing a late free-kick deflected just wide and John Bostock volleying inches past the upright.
Beckford and Becchio were constant threats but Brentford's five-man midfield stifled them at every turn, restricting the chances to just a handful.