The on-loan Sheffield Wednesday defender struck with 13 minutes remaining, diverting the ball into the net with his thigh on only his second appearance for the Lions.
In-form Palace only had themselves to blame as they were 2-0 up and apparently cruising as half-time approached, thanks to a stunning goal from skipper Mile Jedinak and Damien Delaney's header.
But when defender Dean Moxey handled Darius Henderson's header on the goalline, referee Phil Dowd sent him off and Liam Trotter tucked in the penalty to drag Millwall back into the game.
Palace survived with 10 men until the 77th minute, but when Josh Wright swung in a corner Beevers was on hand to bundle the ball home.
The Eagles had bossed the first half until Moxey's moment of madness, with Wilfried Zaha again the most dangerous player on show.
The winger had a £20million price tag slapped on him by chairman Steve Parish this week, and he showed why so many top clubs are watching him with two marauding runs to the byline to set up chances squandered by Glenn Murray and Kagisho Dikgacoi.
Zaha then effortlessly beat two Millwall players out on the wing before curling a 20-yard effort narrowly over the crossbar.
Delaney was also inches from giving Palace the lead when he headed Murray's cross into the side-netting.
The Eagles were living dangerously at the back, though, and could have been reduced to 10 men when Henderson was tripped by Peter Ramage as he was about to burst through on goal, only for referee Dowd to wave play on.
Palace promptly went ahead in the 35th minute in spectacular fashion when Jedinak collected the ball 35 yards out and unleashed a fierce, swerving shot which flew past David Forde and into the net.
Four minutes later they doubled their advantage, Owen Garvan swinging in a free-kick and Delaney rising highest to glance a header past Forde.
However, Millwall were handed a lifeline - literally - by Moxey three minutes before half-time.
The full-back punched Henderson's header from underneath the crossbar to earn a red card, before Trotter calmly rolled in the penalty.
And the Lions almost levelled in first-half stoppage time when Chris Taylor's header rattled the crossbar.
Palace felt they should have a penalty early in the second half when Murray tumbled under Danny Shittu's challenge, but Dowd was unimpressed.
Instead the visitors completed their comeback when Beevers popped up at the far post grab the equaliser, and Palace had keeper Julian Speroni to thank for preserving a point when he denied Henderson in stoppage time.