The quick-silver forward raced through on goal but his cool sidefoot finishes were tipped onto the bar and around the post by home keeper Wojciech Szczesny.
His 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, Sam Saunders seeing a late free-kick deflected just wide and John Bostock volleying inches past the upright.
The draw was always the fairest result, with Brentford closing down the league leaders whenever they pressed forward through Neil Kilkenny.
Beckford and Becchio were constant threats but Brentford's five-man midfield stifled them at every turn, restricting the chances to just a handful.