Johnson decisively struck in the 90th minute to settle a Premier League contest that had up until then seen some dreadful finishing at St James' Park on Sunday.
Newcastle headed into the clash desperate to get one over their rivals having lost each of the last three derbies, but they endured yet more disappointment.
An end-to-end opening half brought plenty of opportunities, with Connor Wickham spurning the best opening when somehow heading wide from two yards.
Jordi Gomez also missed a great chance after the break, while the hosts were similarly wasteful in front of goal.
Newcastle ended the game in the ascendancy, only for Johnson to cap a stunning counter-attack by rocketing a volley beyond Jak Alnwick to beat their rivals in four successive league games for the first time.
The tone was set immediately as Lee Cattermole made a typically robust tackle on Daryl Janmaat after just 10 seconds.
Sebastian Coates was then booked for a strong challenge on Ayoze Perez and Paul Dummett curled the resulting 20-yard free-kick high and wide.
Newcastle remained on the front foot, with Moussa Sissoko hitting a shot straight at Costel Pantilimon after good work from Sammy Ameobi.
The visitors should have been in front midway through the first half, when Wickham headed Johnson's free-kick wide from point-blank range with the goal gaping.
As the yellow-card count began to mount up, so too did Sunderland chances.
Steven Fletcher was the next to go close, rattling the woodwork with a clever, controlled volley from Sebastian Larsson's cross.
Alnwick had to be on high alert soon after to turn Wickham's 25-yard effort around the post.
Both sides continued to pose an attacking threat, with Perez curling a measured shot just wide before Alnwick was called into action to deny Wickham once again.
The second period started on a worrying note, with a bloodied Steven Taylor receiving treatment following a horrific collision with the post having bravely denied Fletcher a seemingly certain goal.
Sunderland almost took full advantage of the defender being off the field to receive stitches, only for Gomez to fire wide with his left foot after playing a one-two with Fletcher.
Newcastle came back into the game and almost opened the scoring when Pantilimon brilliantly tipped Perez's effort over the bar.
The Romanian denied Adam Armstrong moments later, the striker opting to shoot from a tight angle rather than square for the onrushing Sissoko to tap into an empty net.
Johnson then missed the target completely having brilliantly turned Fabricio Coloccini.
The decisive moment finally came in the dying moments of normal time when, after Sissoko had seen an effort tipped over the crossbar, Johnson rifled home at the end of a superb counter-attack.
Newcastle could not find a response, almost conceding again when Larsson found the side-netting after rounding Alnwick in injury time.
