A defensive mix-up saw the home side gift Brentford the lead in a poor first half, but Simeon Jackson levelled after the break.
The Gills pushed for a winner, particularly after Nathan Elder's red card, but Hamer preserved the draw with parries either side of Barry Fuller's sending off.
Ahead of a busy Christmas programme, both teams appeared to be pacing themselves early on with little action at either end.
It took almost half an hour for the game's first shot on target when Brentford took the lead.
Going into the game only Manchester United had conceded fewer league goals at home than Gillingham in the top four divisions, but their normally reliable defence fell apart on 28 minutes.
John Nutter's loose header set Elder through and the striker rounded goalkeeper Simon Royce.
He prodded the ball across the six-yard box but there seemed little danger with Simon King and Garry Richards both on hand to clear the ball.
But disaster struck as the pair left it to each other, allowing Charlie MacDonald to waltz in and tap home.
The Gills improved in the second half and Jackson nodded in Nutter's free-kick on 59 minutes for his 11th goal of the season.
The home side's search for a winner was helped when Elder saw red for pushing King over but Hamer stood firm.
First he denied Richards' firm header at full stretch, before making an even better save from substitute Dennis Oli in stoppage time.
The game ended ten against ten after Fuller was sent off for a stamp on Marvin Williams to incur a three-game ban which, if it stands, would rule him out of Gills' FA Cup tie with Aston Villa next month.