Gary Rowett's side arrived in west London on a three-game unbeaten streak but had no answers to the Bees' fluid football in the first-half.
Vibe poked home from close range before a double substitution at the break saw the tide turn in the Rams' favour.
Jota ended any hopes of a comeback when he rifled home from 20 yards out and Vibe added gloss to the scoreline with his 15th goal of the season.
But there was still time for Jota to add another late on as the Bees put a significant dent in Derby's hopes of a top-six finish.
The Bees may appear to have little left to play for but they began with the bit between their teeth and Sergi Canos danced his way down the left flank before firing a tame cross across the face of goal.
The Spaniard gave Chris Baird, who looked every one of his 35 years, a host of problems and was unfortunate to see an early effort sail over the crossbar after being picked out by Romaine Sawyers' cutback.
Jota was the next to go close, jinking his way into the area and forcing Scott Carson into a low save. The goalkeeper did not manage to push the ball clear of danger but Baird reacted quickest to scramble it away from underneath his own crossbar.
The visitors were restricted to a speculative long-range strike from Bradley Johnson before David Bentley came flying off his line to deny David Nugent, whose composure deserted him.
Hero almost turned villain when Baird contrived to turn Josh Clarke's teasing cross into his own net only for Carson to come to the rescue at full stretch.
But the goalkeeper could do nothing moments later when Jota's deflected shot fell into the path of Vibe, who stroked home coolly from close range.
The impressive Sawyers pulled off an audacious pirouette in the centre circle as Brentford eased through the gears while Nugent shanked an effort wide as the Rams struggled after falling behind.
Rowett responded with two changes at the break as Nugent and Craig Bryson made way for Darren Bent and Will Hughes.
The alterations led to an immediate improvement and Bentley needed to be alert to keep out Thomas Ince's low strike while Jacob Butterfield's scooped effort zipped just over the crossbar.
But, just as the visitors began to turn the screw, Jota produced a moment of class to find the bottom corner and leave Carson rooted to the spot.
Vibe followed suit with a measured finish of his own, sparking a mass exodus from the away end, before Jota wrapped up proceedings at the death.
Derby's revival under Rowett is likely to have come too late but Brentford have cause for optimism that they too could be in the promotion picture next season