Boro’s unbeaten Griffin Park record was ended with just four minutes remaining of the club’s final trip to the current home of Brentford.
An Ollie Watkins goal settled matters after a second half that had seen Jonathan Woodgate’s side twice come from behind in a game where Boro’s character alone deserved a point.
Boro had Dael Fry to thank for keeping the score at 0-0 midway through the half when he was well placed to make a goal-line clearance after a Josh Dasilva header hit the post.
It was a lucky escape for Boro - Dasilva should have scored - and moments later George Saville appeared to have repeated the feat by making a vital goal-line block after a proper scramble inside the Boro box.
This time, though, the ball was adjudged to have crossed the line, and Julian Jeanvier was given the credit for putting the home side ahead shortly before the half-hour.
Marcus Tavernier warmed the hands of David Raya after great work by Marvin Johnson, and it was the latter who almost brought Boro level in the early stages of the second half when his cross-come-shot had Raya scrabbling backwards before getting the deftest of touches to claw the ball to safety.
Lewis Wing also tested Raya with a good strike from just inside of the box before moment later trying again from longer range with an effort which was out of reach of the Brentford keeper, and clipped the post before nestling in the net.
It was no less than Boro deserved - and in front of a sell-out away end as well - but parity lasted barely two minutes. Brentford were back in front when Bryan Mbeumo’s effort appeared to take a huge deflection off Harold Moukoudi which left Pears joylessly scrambling to keep the ball out.
It took just two minutes for Boro to respond, though, Fletcher getting the decisive touch to an in-swinging Tavernier corner to make it 2-2 and level matters for a second time.
It was Fletcher who had a chance to snatch it with 10 minutes remaining when Paddy McNair whipped a ball into the box, but he couldn’t keep the finish down.
In reply, Said Benrahma sent a free-kick over the top and lifted another effort over the bar as the clock started to tick down.
But the game was decided with just four minutes remaining when Watkins showed better composure than Benrahma when presented with a chance to settle matters, and he made no mistake.