In a frenetic and often scrappy lunchtime kick-off, Callum Wilson scored twice from the spot after Luke Ayling opened the scoring and Nick Pope saved from Patrick Bamford, only for Danish defender Kristensen to level late on to boost his side's survival hopes and potentially deliver a blow to the visitors' Champions League aspirations.
With so much at stake for both teams, albeit at different ends of the table, Eddie Howe had spoken on the eve of the game about the importance of the opening exchanges and Joelinton fired over early on, but it was the hosts who struck first.
Rodrigo's header from Patrick Bamford's cross in the seventh minute was well saved by Pope, but Luke Ayling was on hand to tap the ball into the empty net from the rebound to give Sam Allardyce the perfect start in his first home game in charge of the Whites.
Wilson threatened with a shot on the turn after he had held off Kristensen and Miguel Almirón - in for Jacob Murphy in the only change to the team beaten by Arsenal - hit the side-netting, but in the 27th minute Leeds had a huge opportunity to double their advantage.
Junior Firpo made a strong run into the box and Joelinton went to ground in an attempt to win the ball, but instead brought down the former Barcelona full-back and Simon Hooper instantly pointed to the spot.
Bamford stepped up, but Pope dived to his right to parry before scrambling away the rebound to keep his side in the game.
And Newcastle were awarded a penalty of their own three minutes later - and an equally blatant one - when Alexander Isak was felled by Maximilian Wöber. Unlike Bamford, Wilson made no mistake with an inch-perfect finish for his 16th goal of the season.
Just before half time, Almirón curled a left-footed effort just past the far post then early in the second half, Wilson saw a snap-shot deflected over.
As the hour-mark approached, Junior was a little lucky to escape with a yellow card for a late challenge on Bruno Guimarães, with Video Assistant Referee Neil Swarbrick showing leniency towards the Leeds man.
But soon afterwards, Swarbrick urged Hooper to take a look at the monitor when the same player handled in the box from Joe Willock's cross, and the referee awarded Newcastle their second penalty of the day.
Joel Robles was booked for his antics before Wilson stepped up again, but the number nine held his nerve, going straight down the middle to give his side the lead in the 69th minute.
That meant Leeds needed to leave gaps as they pushed to find a way back into the game, and substitute Allan Saint-Maximin had the ball in the net again from Isak's centre, but his celebrations were cut short by a delayed offside flag.
It was the home supporters making the noise in the 79th minute, though, as Newcastle failed to fully clear their lines and were then slow to close down Kristensen, whose effort from the edge of the box took a sizeable nick off Kieran Trippier to deceive Pope.
Saint-Maximin had a shot saved by Robles after a trademark run, and in stoppage time Junior was sent off for a second yellow card after fouling Anthony Gordon just outside the area.
As the resulting free kick was taken, a home supporter confronted Howe in the technical area, with the ball hitting the Leeds defensive wall as the pitch invader was belatedly led away by stewards.
A Fabian Schär volley was then pushed away by Robles in the 98th minute as the game ended all square, and the point could yet prove priceless for both teams.
