Rafael Benitez's visitors opened the scoring as Dominic Calvert-Lewin slotted home a penalty.
But before the break Mateusz Klich equalised to send the home support wild.
Patrick Bamford and Yerry Mina decided to have a wrestling match during the first period too as the frenetic pace of the game threatened to induce violent conduct.
Half-time cooled some heads but Demarai Gray and Raphinha traded goals in the second period to square up before the final whistled called time on an enthralling encounter.
Things didn't immediately go to plan for Leeds as fans got their first taste of top-flight football in more than a decade with Everton taking the lead from the penalty spot.
The Elland Road faithful made thier displeasure unknown when Darren England gave a penalty to the Toffees thanks to a VAR intervention.
Calvert-Lewin may well have grabbed Liam Cooper first but the Scotsman reciprocated and then some, hauling the striker to the ground.
And he happily pointed to the back of his shirt when he thundered the resulting spot-kick home.
Leeds fans may have hated it but ex-Arsenal star Perry Groves hailed VAR getting involved.
"If you're going to use VAR, that is the way that you use it because Darren England was the wrong side so couldn't see it initially," he told talkSPORT 2.
"Kevin Friend has had a look at it and basically he's saying to him 'it's a penalty, come and have a look'.
"They have taken their time and 100 per cent got the correct decision because Liam Cooper has let Dominic Calvert-Lewin get the wrong side of him and stopped him going to play the ball."
Leeds had been swarming all over the Toffees at points in the opening exchanges and the penalty decision, infront of their voiciferous support, seeemed to whip Bielsa's men further into a frenzy.
And seven minutes later it spilled over with Bamford and Yerry Mina clashing by the corner flag.
There were a couple of kicks, some pushing, and some grappling, resulting in a booking each, but Groves felt it was all a bit pantomine.
"That was a bit like wrestling, WWE," he said. "Yerry Mina fell on the floor two or three times, got up and fell back down again.
"To be fair to Mina he kept possession really well by the corner flag and then there was a little coming together with Patrick Bamford. It was playground stuff, to be fair."
Leeds' good play would eventually be rewarded and they levelled four minutes before the break as Klich rounded off a lovely move.
A long ball forward was flicked superbly round the corner by Raphinha, helped on expertly by Bamford and the Polish international found himself through on goal and able to dink into the back of the net.
Their supporters celebrated wildy and only just restraining themselves from running on the pitch, while flares were let off too.
Almost immediately after the break, though, Everton were back ahead as one of their summer signings continues his immediate impact.
Gray, after picking up a pass from Abdoulaye Doucoure, swivelled and shuffled inside the Leeds penalty area before turned and skidding a low shot beyond Illan Meslier.
We're not too sure about the dodgy kneeslide celebration, though.
French starlet Meslier then helped keep the hosts in the game as he twice denied Calvert-Lewin with tremendous close-range stops.
And those saves proved crucial, allowing Leeds to equalise for a second time - and what a leveller it was too.
Cooper laying the ball off to Brazil ace Raphinha and the box and he whipped a ferocious strike beyond the reach of Jordan Pickford.
Everton almost got a late winner as a Doucoure shot deflected just wide with Meslier beaten, while Leeds had a late penalty shout turned down before the final whistle blew on the affair.
There was, though, one unsavoury scene with an object thrown towards Everton's French full-back Lucas Digne.
And Groves condemened the incident, insisting the culprit should be found and punished.
He added: "Let's hope they have got CCTV and whatever idiot has thrown that towards him, or at him, on the pitch is ejected and they get banned for life."
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