The result made it six games unbeaten for both teams, keeping both in the top half of the table and giving neither a psychological edge going into next week's Scottish Cup tie at the same venue.
The home side were quickly into their stride and somehow managed to establish their trademark passing game despite the sodden conditions.
Lee Mair tested home goalkeeper Robert Olejnik with an early half-volley, but his defensive abilities were called into question when Carl Finnigan out-muscled him on the left before shooting just wide.
The spell between the 15th and 16th minutes was electric with Arnau Riera and Thomas Scobbie helping Falkirk to survive a series of Aberdeen attacks.
The Bairns immediately broke up field and top-scorer Michael Higdon hit the side-netting with his left foot.
Riera and Jack Ross both tried their luck from long range as Falkirk began to take control and the offside flag denied them seven minutes before half-time as Higdon looked set to put them ahead.
Aberdeen looked second best, although Scott Severin's volley and a 25-yard free-kick from Barry Nicholson sent out a clear warning to Falkirk.
Lee Miller maintained Aberdeen's momentum at the start of the second period with a sharp turn and shot.
Falkirk then came under further pressure when youngster Scott Arfield was sent off after picking up his second yellow card.
The home fans were furious and the sense of injustice inspired Falkirk to produce their finest move of the match as Dean Holden crossed from the left and Finnigan powered a free header straight at goalkeeper Jamie Langfield.
The Bairns brought on veteran playmaker Russell Latapy in a bid to change the game and within five minutes Scobbie had curled a left-foot free kick fractionally over as Latapy's precise passing stretched the Aberdeen defence.
With nine minutes left, Alexander Diamond failed to cut out Latapy's through ball but Higdon's finish was a massive disappointment.
Both teams went all out to win the game in the closing stages with Dons substitute Jeffrey de Visscher and the outstanding Latapy both shooting narrowly wide.