Booked within seconds of making his debut against Southampton, before earning another rash yellow card against Swansea City, the young striker was given his marching orders after just 16 minutes on Saturday for an apparent stamp on Francis Coquelin.
Arsenal, denied a penalty before Mitrovic’s dismissal, initially struggled to make their advantage count, but broke the deadlock early in the second half when Alex Oxlade-Chamberlain’s shot deflected in off Fabricio Coloccini and the far post.
It was only their third top-flight goal of the campaign, and a second to have come courtesy of an opposing player, but it transpired to be the winner.
Late efforts from Olivier Giroud and Santi Cazorla failed to yield any further goals, which may have provided some concern for Arsene Wenger.
The Arsenal manager had made three changes and opted for Theo Walcott over Giroud up front, despite the Frenchman having scored eight goals in six games against Newcastle, and the visitors started on the front foot.
Arsenal threatened inside the opening two minutes, but Aaron Ramsey overhit his attempted return pass to Oxlade-Chamberlain – in for the injured Mesut Ozil – when Newcastle looked vulnerable.
Tim Krul then had to be alert to snuff out the threat when Walcott looked to nudge the ball past him on the end of Hector Bellerin’s cross.
Bellerin took a tumble in the box following clear contact from Florian Thauvin – making his first league start – after 13 minutes, but referee Andre Marriner was unmoved by Arsenal’s protests.
The hosts already looked up against it before Mitrovic’s match came to a premature end and Arsenal’s dominance increased amid a restless atmosphere inside the stadium as the home fans felt a sense of injustice, though replays showed that the Serb’s studs did scrape down Coquelin’s shin.
As the interval neared, Krul kept out a long-range strike from Alexis Sanchez and then saw Walcott blast the loose ball over the crossbar, but the England forward was offside anyway.
It took just seven minutes of the second half for Arsenal to forge ahead, with Oxlade-Chamberlain’s off-target effort finding the far corner via the unfortunate Coloccini and the woodwork.
With Arsenal having taken 19 points from the last 21 available on the road, the size of the challenge facing Newcastle was evident, but Steve McClaren’s men stuck manfully to their task.
Wenger’s side enjoyed plenty of possession, though rarely opened up their hosts, who showed a level of resolve so sorely missing last season.
Substitute Giroud and Cazorla tested Krul in the final 15 minutes, but Coloccini proved to be the unwilling match-winner as Arsenal made it eight consecutive victories over Newcastle.