Dominic Calvert-Lewin gave the Toffees the lead as he struck from the penalty spot on the half-hour mark. Mateusz Klich levelled for the Whites in the 41st minute, but Demarai Gray put the visitors back in front shortly before halftime.
Playing in front of their first full stadium in the top-flight for 17 years, Raphinha hauled Leeds back for a second time with a wonder goal in the 72nd minute as the points were shared.
Story of the match
It was the visitors who nearly broke the deadlock inside 20 seconds, as Abdoulaye Doucure's long-range strike went just wide of the post. At the other end, Patrick Bamford was picked out in the Everton box with a low cross but saw his strike well blocked.
Luke Ayling then tried his luck from range, seeing his shot deflect for a corner. From the resulting set-piece, the ball was played out to Kalvin Phillips on the edge of the Everton box and his deflected effort was just inches away from finding the top corner.
The Toffees were awarded a penalty following a VAR check as Liam Cooper pulled the shirt of Calvert-Lewin in the box. The Everton forward then stepped up to take the spot-kick and despite Ilian Meslier going the right way, found the back of the net.
Leeds almost hit back within two minutes as Raphinha who scored the winner at Goodison Park last season, fired just wide from 25 yards. The Brazilian tried his luck again from long-range, but with no luck.
Four minutes from halftime, the Whites were level. Bamford broke forward and played Klich in on goal and he slotted past Jordan Pickford to make it 1-1 going into halftime.
The visitors regained the lead five minutes into the second half. Doucoure played Gray into the Leeds box and he managed to squeeze a strike past Meslier and into the bottom corner.
Moments later, Everton almost doubled their lead. Following some neat interchanges Gray found Calvert-Lewin in the Leeds box, but he couldn’t get the better of Meslier. The Whites goalkeeper again saved from Calvert-Lewin after he was played in by Alex Iwobi.
The hosts pushed for an equalizer, winning a succession of corners, with Tyler Roberts' strike from a narrow angle causing the most danger.
The pressure eventually paid off as following another set-piece, Cooper teed up Raphinha, who fired a lovely curling strike into the back of the net to put Leeds once again on level terms.
Leeds then threatened to go ahead for the first time when Raphinha floated a free-kick into the Everton box, but Cooper headed the chance wide. Another Whites free-kick led to another opportunity. Raphinha delivered, with Pascal Struijk heading wide.
Seamus Coleman saw a shot saved by Meslier in the closing stages before Bamford found space in the Everton box but it came to no avail as the referee blew the final whistle.
Man of the match: Abdoulaye Doucoure
He was so close to winning it late on for the visitors and his play in the midfield was outstanding throughout the entire game.