The promotion chasers recovered from conceding an early goal to stroll to a comprehensive home win after a first-half triple strike.
The game may have been different if Morecambe had held on to the lead given to them by Stewart Drummond in the fifth minute.
The midfielder arrived late to steer home a Rene Howe knock down, but the visitors were soon reeling as Brentford hit back.
Charlie MacDonald rounded off a great move involving Glenn Poole and Marcus Bean to level things three minutes later.
And Poole gave the home side the lead from a MacDonald cross in the 11th minute to cap an amazing start to the evening.
Nathan Elder completed the scoring inside the first 35 minutes when he headed home a MacDonald cross, but Brentford will wonder how they did not extend their lead.
Elder headed wide from close range, MacDonald fired across the face of goal from a tight angle after rounding Morecambe goalkeeper Barry Roche and Poole missed the best chance of the evening when Roche saved his penalty after Elder had been barged over by Jim Bentley.
Poole also forced Roche to tip a long-range free-kick onto the post and Marvin Williams brought another save from the Morecambe stopper with a fierce low shot.
But Morecambe also posed a threat as Neil Wainwright hit the bar with a cross which almost caught Brentford goalkeeper Ben Hamer out and Bentley had a header cleared off the line.
The visitors thought they had scored when Aaron Taylor headed a Howe nod-back past Hamer but Bean cleared off the line.
And that summed up their evening as the home side continued their march towards the top of the table.