Mike Riley brandished the red card for what he adjudged to be a headbutt by the Toffees record signing on Chelsea centre-back William Gallas.
At first sight it seemed a harsh decision, but replays showed an over-zealous Beattie had, in fact, led with his head.
Everton fans and players greeted the decision with equal levels of fury and disbelief and Gallas was back on his feet minutes later to a cacophony of boos.
Chelsea used the bad blood to their advantage, craftily carving out a chance for Damien Duff on 14 minutes. Joe Cole and Eidur Gudjohnsen moved the ball left across the edge of the Everton box before Duff fired a powerful left-footed drive narrowly over the bar.
Minutes later Jose Mourinho's men carved open the Toffees defence again, but Tiago wastefully lofted a glorious chance high over the bar from seven yards out.
With 25 gone Duff teased Alessandro Pistone down the Everton right before whipping in a dangerous low cross which Nigel Martyn only just managed to tip away from the waiting Gudjohnsen.
Duff was a constant threat down the left for Chelsea and as the half moved on Cole, enjoying a rare start in the absence of Arjen Robben, fashioned a couple of long-distance chances for himself.
Everton reverted to a 4-4-1 formation pushing central defender Joseph Yobo out on to the right wing and deploying Marcus Bent in his preferred lone striker role.
Bent looked lively and selflessly chased every lost cause, but against the best defence in the Premier League, or any other league for that matter, the Blues struggled to make an impression due to a chronic lack of attacking numbers.
The spirit and work-rate that has served them so well all season, and a string of excellent Martyn saves however, ensured that they ended the half on level terms.
In the second period Chelsea immediately penned Everton back into their own penalty area. Martyn's agile reactions and a clearance from David Weir denied Gudjohnsen from two yards after Duff had whipped in another dangerous cross-cum-shot.
Another sweeping Chelsea move on 55 minutes saw Frank Lampard's toe-poke expertly saved by Martyn at full-stretch after Claude Makelele and Cole had combined to play the England man in.
The Chelsea pressure was relentless and with 20 minutes left they finally made a long overdue breakthrough. Gallas surprised the Toffees rearguard by popping up in the box.
His side-footed flick from Paulo Ferreira's cross clipped the bar but bounced to an unmarked Gudjohnsen who duly tapped in the opener from two yards out.
With eight minutes to go Lee Carsley headed Everton's first significant chance of the game goalwards from a Kevin Kilbane free-kick,
Record breaking keeper Petr Cech showed why he has gone so long without conceding by gathering up the Irishman's nod with assured ease.
Duncan Ferguson's introduction gave the Goodsion Park faithful hope as the Blues resorted to pumping long balls towards their talismanic cult hero. Chelsea looked flustered and John Terry was booked for throwing the ball away as he tried to buy his side some precious moments to re-group.
Ferguson's presence forced a panicked Gallas into a deliberate hand-ball on the edge of the box, but new signing Mikael Arteta struck the resultant free-kick straight into a steadfast Chelsea wall.
There were vehement appeals for a penalty when Gallas again looked to have handled in the area. But in the end Everton's drive and determination was not good enough to break the Stamford Bridge boys' resolve.
Mourinho's juggernaut steams ever nearer to a seemingly inevitable title. But for David Moyes the procession of dropped points must now be a concern as he peers worryingly across Stanley Park to see how the red half of the city fair in their Champions League charge.
Man of the match: Damien Duff - The Chelsea winger was a constant thorn in Everton's side as he expertly took over the attacking reigns in the absence of Arjen Robben. Equally as effective on either flank the Irishman teased the Toffees defence with a string of darting runs.