The Gunners rose to second in the Premier League table thanks to their nervy beating of Nuno Espirito Santo's side, where Gabriel Jesus and Bukayo Saka made the net bulge before Taiwo Awoniyi's consolation.
Arteta's men endured 45 minutes of frustration in the first half, failing to penetrate a sturdy Forest backline, but Jesus managed to poke the ball through Matt Turner's legs from an incredibly tight angle to propel the Gunners ahead in the 65th minute.
Arsenal capitalised on another defensive error from Forest to double their lead just seven moments later, as with several Tricky Trees players in the Gunners half following a corner, Gonzalo Montiel's lackadaisical pass fell at the feet of Martin Odegaard, and a quick Gunners counter ended with Saka firing home across goal.
Arsenal were full value for a 2-0 lead owing to their patience and persistence, but Forest found a lifeline through Awoniyi, who got a lucky break of the ball after outmuscling William Saliba in the 89th minute.
Nevertheless, Arsenal survived over seven minutes of stoppage time to travel home with maximum points - ending a three-game losing run at the City Ground - but cameras picked up full-backs Zinchenko and White having a spat at full time.
Set-piece coach Nicolas Jover stepped in to separate the pair, while Arteta and Zinchenko were also involved in an impassioned discussion on the field, but the Spaniard simply saw two players "demanding more" from one another and was only too happy to witness the heated exchange.
"I love it. They are demanding more from each other," Arteta told reporters in his post-match press conference, as quoted by football.london. "They are not happy with the way they conceded and they are just trying to resolve it. It got a bit heated. But that means that it's enough. Playing the way we played the result has to be bigger and the clean sheet has to be there."
While White and Zinchenko were dissatisfied with one another after the final whistle, the travelling Arsenal fans were in a buoyant mood once the team sheets were released, as Emile Smith Rowe was brought in for a surprise start.
Thanks in no small part to injuries, the 23-year-old has failed to kick on since his breakthrough 2021-22 season, but he was given the nod over Kai Havertz to join Odegaard and Declan Rice in the Gunners' engine room at the City Ground.
Making just his second Premier League start of the season, Smith Rowe lasted for 71 minutes, during which he completed 93% of his passes and fired one curling strike over the bar in the first half.
Arteta is said to have been left hugely impressed with Smith Rowe's performances in training during Arsenal's recent warm-weather camp in Dubai, and the Gunners boss hailed the Englishman as a "joy to watch" after his City Ground cameo.
"I thought he was really good. I think he looked exactly the same as he looks in training and every time we've put him in. He fully deserves his chance," Arteta added.
"He's really put his head down, his attitude has been really good. He's a tremendous player and you see the way he moves. It's just a joy to watch him."
Arsenal now only have a two-point gap to make up to Liverpool, who can restore their five-point lead by beating Chelsea on Wednesday, while they are three points better off than Manchester City having played two more games than the champions.
The Gunners now have four full recovery days before hosting Liverpool at the Emirates in Sunday's mouthwatering top-of-the-table showdown.