The Colombian winger, who scored his first goal for the club since his summer move from Feyenoord in the EFL Cup last week, struck 18 yards after the break as Leeds piled the pressure on Everton.
They improved considerably after a poor first half when Anthony Gordon scored his second successive goal and kept his composure to slot the ball through Alex Iwobi’s through ball into the legs of Alan Meslier.
Leeds top scorer Rodrigo also appeared to have a shoulder injury after an innocuous challenge on Everton goalkeeper Jordan Pickford.
But inspired by the impressive Jack Harrison and substitute Joe Geilhardt, Leeds challenged both the players and Brendan Aaronson as they tore through their opponents to find Pickford in fine form.
As the game progressed, Everton had late chances to win thanks to Amadou Onana and Nathan Pietersen.
But Everton’s backline held firm with Leeds adding pressure, although the result would set the Toffees in search of their first win of the season under Frank Lampard.
Leeds stepped up in style in the second half
Leeds bounced back in the second half after a first half in which they scored a number of tries but found Everton’s new defense very difficult to break down.
Rodrigo’s injury also dented his confidence as the Spain international left the pitch in pain after taking a shoulder shot alongside Pickford.
He had the best chance of the first half, getting inches from an early Harrison cross, but it wasn’t until after the break that the hosts began to test Pickford.
First Aaronson made a good save from the Everton keeper before Harrison saved another effort.
But the English number one couldn’t do much against Sinestra’s effort from the edge of the penalty area.
Elland Road then erupted and threatened to be swept away as Gordon and Rasmus Christensen clashed moments later, both yellow cards and benched.
At times it felt like a return to another away side but the football was exciting even if Patrick Bamford’s return from injury failed to produce a winner.
Despite the disappointment at the end, Leeds showed they mean business under boss Jesse Marsh as they fell to fifth in the table with their first defeat of the season at Brighton on Saturday.
Everton missed a shot as Maupe was dropped.
Although Lampard was frustrated that his side failed to convert their chances late on, Pietersen managed to block a clean shot on goal by Meslier, showing enough defensive ability to secure a point from his side. .
Gordon, who was the subject of at least one rejected £45m bid from Chelsea during the transfer window, has shown his intelligence and why Lampard is keen to keep England Under-21s.
But the third draw of the season was also credited to a revamped defence, held together well by new centre-back duo Conor Coady and James Tarkowski. They were well protected by the summer signing of Onana, who looked impressive at the base of midfield.
This part of Lampard’s squad improved dramatically last season, but where they still struggled to score, even denied a narrow offside decision when Demarai Gray put the ball into the net. gave .
With Dominic Calvert-Leon still injured, the arrival of Neil Mape from Brighton on Friday will help that cause, but he was left on the bench in frustration when Everton missed out on a late afternoon move for him.