The Bees looked set to spoil the title party at Kenilworth Road as strikes from Sam Sodje and Deon Burton cancelled out Ahmet Brkovic's fifth minute opener.
But after twice hitting the post and seeing visiting goalkeeper Stuart Nelson make some outstanding saves, champions Luton were rewarded with an astonishing late flurry.
The win avenged two defeats at the hands of Brentford earlier in the season and sets Town up for a record 100 points finish to the season if they win their final game at Doncaster next week.
The Hatters started well and went ahead in the fifth minute when Paul Underwood crossed, Steve Howard flicked on and Brkovic arrived at the far post to fire the ball into the ground and up and over visiting keeper Nelson for his 16th goal of the season.
Marlon Beresford had to be alert to palm aside a 20-yard Stewart Talbot effort in the ninth minute before Howard headed Robinson's right-wing cross just wide three minutes later.
But Brentford began to make their aerial threat count and after Ed Hutchinson had headed just over in the 17th minute, the Bees equalised in the 20th minute when Beresford could only half punch clear John Salako's centre from the left and Sodje headed home.
The visitors went 2-1 ahead in the 26th minute when Michael Turner intercepted a Nicholls pass and ran unchallenged for 50 yards before playing in Burton to calmly slot past Beresford from just inside the penalty area.
Howard almost levelled after a determined run and pass from Sol Davis found the big man in space in the penalty area, but Howard's left-footed shot from eight yards ended up just the wrong side of the post.
The Hatters started the second half just as they had the first and they almost equalised two minutes in when Nicholls saw a curling free-kick from the edge of the penalty area bounce back off the post.
Nelson saved from Howard and Underwood and Howard hit the post before Nicholls finally equlised with six minutes remaining, converting from the spot for his 13th goal of the season after Michael Turner had fouled Robinson in the box.
Luton went 3-2 ahead in dramatic style when Curtis Davies nodded on Robinson's corner and Showunmi headed the ball over the line.
There was still time for Robinson to grab a fourth in the third minute of added on time when he side-footed home substitute Rowan Vine's pull back from 15 yards to send the Luton fans wild with delight.
The win was the perfect platform for Town to officially receive the Coca-Cola League One trophy after the final whistle amid jubilant scenes on the pitch.