Ivory Coast international Pepe capitalised on a nervous start to the game by Ole Gunnar Solskjaer's side, who lost for only the second time in 10 league games after failing to expose Arsenal's flaws in the way Chelsea had done in a 2-1 win on the same ground three days earlier.
Sokratis Papastathopoulos doubled Arsenal's lead just before half-time and the hosts' improvement was testament to Arteta's impact on a squad that has appeared disjointed for much of this season.
The revived performances of Mesut Ozil and Granit Xhaka in the Gunners' midfield will have particularly pleased the coach, who delivered Arsenal's second victory in 13 gruelling Premier League games that had seen them drop into the bottom half of the table, this result lifting them back up to 10th and offering cause for optimism at the start of 2020.
Marcus Rashford sent a shot dipping into Bernd Leno's arms from 25 yards in the first minute as United showed their threat on the break.
But Pierre-Emerick Aubameyang's trickery set Sead Kolasinac free in the United box after just eight minutes and his cross deflected into the path of Pepe, who swept into the net from 12 yards to get the hosts off to an excellent start.
Pepe went agonisingly close to doubling Arsenal's lead seven minutes before half-time when David de Gea's careless clearance fell to him 20 yards out and he curled a shot onto the post with the United goalkeeper flailing.
But Arsenal kept the pressure on an embattled United defence and got their reward when Alexandre Lacazette flicked a corner into a crowd of defenders before it bounced to Sokratis, who lashed it high into the net from close range.
Fred tied his luck with a rising shot from 25 yards 10 minutes into the second half, but Leno claimed it comfortably as United struggled to create the space they needed to trouble Arsenal.
Nemanja Matic did carve out an opportunity with a clever ball into the area a few moments later but substitute Andreas Pereira hit the side-netting with his angled effort.
A foot injury to Kolasinac was the only fly in the ointment for Arsenal, who will hope this victory marks the beginning of a push towards a place in the top six that only recently looked very much beyond them.