Skipper Andrew Considine, who along with top scorer Scott Vernon signed a new deal to remain at Pittodrie this week, was called into action early on, heading away a dangerous Dean Shiels corner.
The hosts had their first shot on goal after nine minutes but Bell comfortably saved Chris Clark's low drive.
The visitors went much closer after 20 minutes when Garry Hay stung the palms of Brown with a powerful effort from 25 yards.
The Dons grew in confidence as the half wore on with a Fraser Fyvie shot bravely blocked by Hay, with Kari Arnason heading over from the resulting corner.
Aberdeen had a scare at the other end when Brown fumbled a Shiels shot but the Welshman managed to gather the ball at the second attempt with Liam Kelly ready to pounce.
New Dons loan signing Mark Reynolds made a surging run past two Kilmarnock defenders early in the second half before dragging a shot wide of the target.
Brown looked nervous again as he fumbled a Danny Racchi shot when he should have made an easy save.
Killie midfielder Racchi was unlucky not to get the opener after 66 minutes when his delicate chip narrowly cleared the Aberdeen crossbar.
A Dons corner from Ryan Jack picked out Rory McArdle but the defender's header could only find the side-netting.
The visitors who should have won it at the death when Heffernan went through one-on-one with Brown but the Irishman shot straight at the advancing goalkeeper.