The Blues slipped back into the bottom half of the table after losing their record third west London derby at home in a row to the Bees on Saturday afternoon.
Pinnock's header was against the run of play but Chelsea only had themselves to blame for being wasteful and got stung by Thomas Frank's men.
Cole Palmer was the one positive but Chelsea go into a high-pressure match next Monday against table-toppers Tottenham in, at best, 11th place.
Nizaar Kinsella was at Stamford Bridge witnessing the action.
Robert Sanchez - 7
Made a stunning late save but there was nothing he could have done with the goal.
Axel Disasi - 5
Playing at right back, battled Bryan Mbeumo excellently but offered very little in attack.
Thiago Silva - 7
Very good in possession, threatened at set-pieces and dealt with Brentford's aerial threat.
Levi Colwill - 7
Outstanding against a physical forward line and gave nothing away.
Marc Cucurella - 6
Missed the chance of the first half but it fell on his weaker right foot in an unnatural striking position. A good defensive and creative display, though.
Moises Caicedo - 5
An underwhelming display in possession.
Conor Gallagher - 7
His excellent long-range shot was saved in the 12th minute.
Raheem Sterling - 5
Looked good on the break and beat his man regularly but, with so little space available, failed to cause real damage.
Cole Palmer - 9
Devastating creating chance after chance in the early moments as a no10. He was by far Chelsea's most impactful attacking force.
Noni Madueke - 5
Hit the bar with a wonderful effort from the edge of the box early on. He was threatening at times, but also wasteful in other moments. Taken off in the 67th minute.
Nicolas Jackson - 4
Had a good early effort but was anonymous afterward.
Ian Maatsen - 5
Out of position, Pochettino's utility man is always tidy but couldn't turn the tide.
Reece James - 7
A logical change and had an impact with his crossing, creating a late chance.
Lesley Ugochukwu - 5
A sign of a lack of options to bring a defensive midfielder on when chasing a goal.
Deivid Washington - 6
Made his senior Chelsea debut in a brief cameo and got his chance to win the match.
Unused substitutes Eddie Beach, Djordje Petrovic; Malo Gusto, Benoit Badiashile; Alex Matos.