Relegated Burnley had taken just two points from their first three games, and looked to be heading for another difficult afternoon as the Bees tested home stopper Tom Heaton.
But Keane’s first-half header, against the run of play, proved to be enough to inflict a first league defeat on Brentford head coach Marinus Dijkhuizen.
Brentford had the best of the early exchanges and Akaki Gogia’s quick feet won a free-kick on the edge of the penalty box after 16 minutes – Heaton parrying Alan Judge’s effort clear.
Burnley captain Heaton was called into action again moments later, this time taking two attempts to claim Lasse Vibe’s low strike after the winger’s clever turn in the box.
Vibe was in again midway through the first half, racing on to Konstantin Kerschbaumer’s defence-splitting pass, but Heaton stuck out a leg to save his low strike.
Having rode their luck, the hosts took the lead against the run of play, however, as Keane’s back-post header, from David Jones’ corner, snuck in after 26 minutes.
That goal invigorated the Clarets, and Scott Arfield had time and space to double the lead 10 minutes before the break but blazed wildly over when Michael Kightly’s cross was only half-cleared.
At the other end, Alan McCormack’s clever one-two with Vibe gave him space to shoot, but Heaton comfortably held his low left-footed effort.
Burnley were much brighter after the break, and Harlee Dean had to be at full stretch to clear George Boyd’s header behind as Lukas Jutkiewicz waited to tap in after 53 minutes.
Two minutes later, Jones headed David Button’s unconvincing clearance into Arfield’s pass, but the back-pedalling keeper turned his first-time shot wide.
Clarets substitute Sam Vokes had space in the area after 70 minutes when Kightly headed into his path, but the Wales striker shot just over.
Moments later Jutkiewicz showed good strength to hold off the defenders and run onto a long ball but he could not keep his strike down.
Still Burnley pushed for a second, however, and Matthew Taylor – on for Kightly – fired a hard, low free-kick wide of the far post with just under 15 minutes remaining.
Marvin Sordell then ran onto Boyd’s header on, but Button gathered his low strike across goal at the second attempt.
Brentford’s response to the onslaught of pressure was to shuffle the midfield, but they could not break down the stubborn Burnley defence.
With chances at a premium, Kerschbaumer’s long-range effort with three minutes to go was as close they came to an equaliser – but his effort dropped just over.
And Burnley stood firm to bag a much-needed first victory of the season.