Former Sky Blue Robbie Simpson had put the West London side ahead in the 31st minute with a second for Woodman four minutes later.
The second half belonged to Cheltenham and Jeffers who is on loan from Coventry City for a month, smashed in a shot from a rebound in the 61st minute to set up a grandstand finish and earn himself the Cheltenham Man Of The Match award but Brentford held on to win.
Coventry City's defeat at Morecambe was not the only shock in the League Cup 1st Round.
Nottingham Forest lost 2-1 at Bradford City after extra time, Barnsley lost 1-0 at home to Rochdale, Derby lost 1-0 at Crewe, Doncaster were beaten 2-1 at home by Accrington, Northampton beat Brighton 2-0, Oxford beat Bristol Rovers 6-1, QPR lost 3-1 at home to Port Vale, Shrewsbury beat Charlton 4-3, Bristol City lost 3-2 at Southend after extra time,