Class act French forward Saint-Maximin struck in the 44th minute to bag the Magpies a point after Raphinha had given Marcelo Bielsa's Whites a 13th-minute lead.
Both sides had a host of chances to win the contest, particularly in a chaotic first-half of attack versus attack.
Saint-Maximin had five shots on goal himself with four efforts saved by Illan Meslier and another blocked as part of 17 attempts for the Magpies, seven of which were on target.
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Leeds - who had 65 per cent possession - served up 22 shots on goal, of which nine were on target.
But the Whites and Magpies were both forced to settle for a point of which 24-year-old Saint-Maximin said he was disappointed, despite coming against a "really great team."
Leeds only have three points for the current Premier League campaign, one more than Newcastle, but Saint-Maximin has not forgotten the Yorkshire outfit's ninth-placed finish last season and results such as a 2-1 victory at champions Manchester City.
Assessing whether Friday's draw was a case of a point gained or two dropped, Saint-Maximin told NUFC TV : "To be honest, for me, it's two lost because we did everything in this game to win the match.
"We had a lot of chances.
"We were brave, every player played really well.
"It's difficult to start a game 1-0 down against Leeds and I think we tried to do everything for a comeback.
"We scored and afterwards we had a lot of chances to make it 2-1 so we are really disappointed."
Turning his attention to the opposition that his Magpies were facing, Saint-Maximin added: "The players gave everything.
"You don't forget that Leeds is a really great team.
"They played a really great game against the big teams - City, Chelsea, Liverpool, you can see that last season.
"It's a tough team, it's a tough team to play against and I think we showed a lot of quality to win the game.
"We had more chances than Leeds.
"We just have to keep going because every player was brave and I hope we keep going to play like this."
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Thank you Laura Collins