Striker Kuffour, who scored his first two goals for the Bees in a 2-2 draw with Huddersfield at Griffin Park in August, returned to haunt the home side.
Huddersfield striker Andy Booth had a hat-trick of first half chances and the Terriers could have had the game wrapped up before the interval.
However, tricky winger Charlie Ide rocked the home side with a stunning 25-yard curler four minutes into the second half.
Kuffour then sealed it with a close-range finish nine minutes later as Scott Fitzgerald's men boosted their hopes of beating the drop.
Huddersfield dominated the first 25 minutes of the game and with new recruit Frank Sinclair showing his Premiership pedigree the home side were in control.
Booth set the tone for a frustrating afternoon when he sliced his shot with the goal at his mercy.
Michael Collins fired just wide before Booth missed what is usually bread and butter to him.
Andy Holdsworth produced a top drawer cross which found Booth unmarked. He could have picked his spot but his header flashed beyond the far post.
Gary Taylor-Fletcher almost repeated the feat when he charged forward from his own half and cut through the Bees defence only to lash a shot just over.
Kuffour had a chance when Paul Brooker found him in the clear. The striker cut inside a defender and fired across goal but keeper Matt Glennon saved with his out-stretched boot.
Booth had another good chance with a diving header which he again planted wide but an assistant referee had flagged for offside.
A minute from the break, Neil Shipperley wriggled free in the box and, with only Glennon to beat, blasted against the foot of the near post.
Brentford were on their way to their first hat-trick of wins in more than a year when Ide's left-footed curler from outside the box found the back of the net.
Joe Keith allowed Kuffour to grab his 13th goal of the season with a defence splitting cross which had Brentford players queuing up in the middle in the 58th minute.
After that, Brentford boss Fitzgerald was determined to cling on to the three points and took off both scorers.
Huddersfield finished strongly but never threatened to get back in the game.
Booth squandered another straightforward header and keeper Nathan Abbey was called into action for the first time in the game as he twice denied Danny Schofield and then blocked from substitute Chris Brandon.