Marcello Trotta scored the only goal of the game in first-half stoppage time with a shot from 20 yards, but Brentford had centre-back James Tarkowski sent off after a lunge on Romain Vincelot.
Despite their numerical disadvantage, though, Mark Warburton's side held on and they are now only a point behind Wolves at the summit.
The leaders retained a slim advantage as they drew 0-0 with Shrewsbury Town - their club record nine-match winning run finally ended as they were frustrated at Molineux.
The hosts almost snatched the points deep into the second half but substitute Matt Doherty saw his header cleared.
Orient, meanwhile, have played two games more than their rivals and now lie in third.
Elsewhere, Britt Assombalonga scored a double as Peterborough United beat MK Dons 2-0 to give their play-off hopes a lift.
Assombalonga turned home Michael Bostwick's cross for his first and then converted from the penalty spot two minutes later after George Baldock had brought down Conor Washington in the area.
Cody McDonald earned Gillingham a 1-1 draw against Bradford City, with both teams level on points in mid-table.
Ten-man Swindon Town had to hold on to earn a point from a 0-0 draw against Bristol City, with Jay Emmanuel-Thomas hitting the post for the hosts before midfielder Alex Pritchard was shown a straight red card for pushing Wade Elliott.
Meanwhile, Stevenage frustrated Carlisle United in a goalless draw while Mike Jones' solitary goal was enough to keep Crawley Town's slim play-off hopes alive with victory over Colchester United and Crewe Alexandra shared a 1-1 draw with Oldham Athletic.
Rotherham United left it late to snatch a point from their own 1-1 draw with Walsall, substitute Nicky Adams scoring a minute from time to cancel out Milan Lalkovic's 19th-minute opener.
But things look bleak at the bottom for Notts County, whose survival chances were dealt a major blow when Steve Jennings' late goal condemned them to a 3-2 defeat against Tranmere Rovers.
Rovers jumped out of the relegation zone as a result, while County are now mired at the bottom, seven points adrift of safety having played a game more than most of their rivals.
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