Leeds went ahead in the 13th minute when Raphinha whipped in a cross from the right flank that sailed past Magpies keeper Karl Darlow into the bottom left corner after Rodrigo had jumped over the ball.
The contest then became a crazy match of attack versus attack and Newcastle were denied by the frame of the goal as a Matt Ritchie effort from 20 yards out flew back off the post.
But the hosts drew level one minute before the break when Joelinton worked the ball to Allan Saint-Maximin who moved wider and wider before unleashing a fine finish into the bottom left corner of the net.
Both sides then had chances during the second half in which Crysencio Summerville was handed a Whites debut but neither team was able to find a winner in their search for a first win of the new Premier League campaign.
Graham Smyth, the YEP's chief football writer, hands out the scores.
7. Mateusz Klich
6 - Busy but not spectacular. Got into good positions, linked play but didn't have his shooting boots. Photo by LINDSEY PARNABY/AFP via Getty Images.
8. Raphinha
7 - Leeds' best attacking threat, got into positions to hurt the hosts and was left unmarked but should have scored more than the somewhat fortunate one that went in. Photo by LINDSEY PARNABY/AFP via Getty Images.
9. Dan James
5 - Unable to find the same space that Raphinha enjoyed, couldn't get past his men and couldn't take the chances that came his way. Picture by Bruce Rollinson.
10. Rodrigo
6 - A strange performance. Some really poor stuff, some good stuff in attack. Created a great chance for Bamford and for Raphinha. Didn't contribute too much defensively. Photo by LINDSEY PARNABY/AFP via Getty Images.
11. Patrick Bamford
7 - Lots of running, lots of defensive effort. Didn't take the chance Rodrigo created for him on his right foot. Came deep to link play well. Photo by Stu Forster/Getty Images.
12. Tyler Roberts (sub)
5 - Another game in which he was unable to add the impact Leeds needed from him. It wasn't for lack of trying, kept getting on the ball. Photo by Ian MacNicol/Getty Images.