It was Rotherham's fourth game without a win as the slide well down the table continued, following their ten-point deduction for slipping into administration with crippling financial problems.
And with the administrator warning the club needs regular attendances of 4,000 to survive, less than 3,000 of the home side's hardcore turned up.
Rotherham came close to an early opener when Ian Ross smashed a goalbound shot, but it struck his own team-mate Tom Cahill and looped out.
Cahill, showing clever touches, set up Danny Harrison but he smashed his shot over the top before a Derek Holmes header brought a save from Simon Brown.
A Marc Joseph cross broke back to Ross, but his 25-yard effort was volleyed over the top and after 26 minutes the home side should have gone in front.
A blistering shot from Mark Hudson beat Brown but a tremendous diving header on the line from Alan Bennett denied Rotherham.
Despite surrendering much of the possession, Brentford produced two superb chances.
The first saw Wayne Brown latch on to a low ball from Ryan Dixon but his fierce shot was turned away by keeper Andy Warrington.
But six minutes before the break the visitors went ahead. Ricky Shakes headed on a Ryan Dickson cross and Elder found himself in space and drilled in a low shot to claim the lead.
Elder came within a whisker of adding a second goal but was inches short of sliding in a low cross from the left.
Elder was well positioned as Rotherham were caught out at the back after 69 minutes, but he headed wide of the target after a cross from Gary Smith.
Rotherham came close to an equaliser after 73 minutes when the ball broke to Jamie Green, but Craig Pead hurled his body in to block the shot.
The Millers finally levelled with a deflected shot from Hudson three minutes from the end, but substitute Connell - who had only been on for six minutes - grabbed the injury-time winner for the Bees.