Playing barely 48 hours after a long trip from London at the end of the Premier League season, the two sides nevertheless put on an entertaining show at the cavernous Melbourne Cricket Ground.
Maddison fired Spurs ahead in the 32nd minute before Alexander Isak netted to level the scores on the cusp of half-time.
With mass changes after the interval, neither side could deliver the winner with the game ending 1-1 and going to penalties, which appeared to be a surprise to the players.
Spurs' winger Bryan Gil's opening effort was saved, with Newcastle making no mistakes to win 5-4.
"It was a decent game, the first half was all good and the second half did feel like a friendly," said Tottenham boss Ange Postecoglou. "But I think there was enough there for the punters to get something out of the game."