Leeds lost captain Liam Cooper to injury inside the opening quarter of an hour but United went ahead in the 27th minute when Tyler Roberts flicked home a Raphinha cross.
Brentford equalised nine minutes after the break as Shandon Baptiste converted from the middle of the box, shortly after United star Kalvin Phillips had pulled up injured and was eventually replaced by Mateusz Klich.
The Bees then bagged what looked set to prove the game's winning goal seven minutes later when a Bryan Mbeumo through ball played in Sergi Canos who smashed home a clinical finish past Illan Meslier.
But Bamford returned from two and a half months out through an ankle injury as United's third and final substitute in the 68th minute and kneed home a corner in the 95th minute with a finish that flew in off the underside of the bar.
Graham Smyth, the YEP's chief football writer, hands out the scores from another dramatic game at Elland Road.
. Leeds United shared a 2-2 draw with Sunday's Premier League visitors Brentford at Elland Road.
PERFECT START: Tyler Roberts celebrates as Dan James, left, comes to join the Whites forward after firing Leeds United ahead in Sunday's Premier League clash against Brentford at Elland Road. Picture by Tony Johnson.
. Illan Meslier
7 - A spectator for much of the game. Couldn't do much about either goal. Produced a big header outside his area when called upon Photo by George Wood/Getty Images.
. Luke Ayling
6 - Rusty. Lots of effort, tried to get on the ball lots and provided the flick-on for the equaliser. Guilty of some poor passing. Photo by Laurence Griffiths/Getty Images.
. Liam Cooper
N/A - He looked relatively comfortable before he went off, even if Leeds weren't playing that well. Photo by Stu Forster/Getty Images.
. Diego Llorente
6 - Was beaten on his blindside by the run of Canos for the second goal. Another who wasn't as good as he can be on the ball. Photo by Stu Forster/Getty Images.
1. Illan Meslier
7 - A spectator for much of the game. Couldn't do much about either goal. Produced a big header outside his area when called upon Photo by George Wood/Getty Images.
2. Luke Ayling
6 - Rusty. Lots of effort, tried to get on the ball lots and provided the flick-on for the equaliser. Guilty of some poor passing. Photo by Laurence Griffiths/Getty Images.
3. Liam Cooper
N/A - He looked relatively comfortable before he went off, even if Leeds weren't playing that well. Photo by Stu Forster/Getty Images.
4. Diego Llorente
6 - Was beaten on his blindside by the run of Canos for the second goal. Another who wasn't as good as he can be on the ball. Photo by Stu Forster/Getty Images.
5. Junior Firpo
6 - Gave the ball away for the second Bees goal. Wasteful in possession at times but got forward well in the first half. Photo by George Wood/Getty Images.
6. Kalvin Phillips
7 - Played with an edge in the first half, seemed riled but did well. Injury took him out of the game and cost Leeds his influence. Picture by Tony Johnson.