It was a case of deju vu for Newcastle.
Liverpool snatched a dramatic late victory at St James' Park with a stoppage-time goal last month, and Arsenal followed suit on Sunday.
Leading in the 83rd minute, Newcastle will rue how they did not at least come away with a point after conceding two late goals, particularly after finding a way to take the lead from a set-piece of their own.
Newcastle had been struggling to fire from set-plays in the opening weeks of the season despite the obvious height in the side.
But in a clever short routine Tonali played a one-two with Anthony Gordon before swinging over a cross.
The towering Woltemade barely had to jump to score his second goal in three league games since completing his club record £69m move from Stuttgart last month.
With his side in front, the German was given a standing ovation when he was replaced by William Osula midway through the second half.
But Newcastle looked affected by defender Tino Livramento coming off on a stretcher after landing awkwardly.
Newcastle had not conceded a goal from a set-play in the opening weeks of the campaign, but were ultimately undone by two corners.