Sandro Tonali wheeled off in celebration in stoppage time when his speculative effort went through a sea of legs and into the net to win a rollercoaster of a match in Debrecen.
Germany take a narrow one-goal lead into the second leg of the UEFA Nations League quarter-final against Italy.
Eddie Howe's men are languishing in 10th place in the Premier League with 10 games to go and any hope of the club's first major trophy since 1969 is over for another year.
Newcastle United have spent a net 95 million pounds ($121 million, 110 million euros) this transfer window in signing Sandro Tonali, Harvey Barnes and Tino Livramento, with Allan Saint-Maximin having left St James' Park.
Premier League clubs have splashed out over $1.3 billion on fresh faces ahead of the new season.