Gabriel Jesus and Bukayo Saka were on target at the City Ground as the Gunners moved to within two points of Liverpool, who they face at the Emirates on Sunday.
Liverpool can stretch their advantage at the top once more when they host Chelsea on Wednesday.
Arteta's men had not won away since early December as their push for a first title in 20 years stumbled over the festive period.
But they have won both their games since returning refreshed from a two-week winter break.
"We have to generate some momentum," said Arteta. "We have to prepare well as it is going to be a big game (against Liverpool).
Forest had won all of the previous three meetings between the sides at the City Ground, including the defeat that mathematically ended Arsenal's title challenge last season.
But Nuno Espirito Santo opted to just try and contain Arsenal and Forest's gameplan was undone once Jesus broke the deadlock 25 minutes from time.
"Against this team at home I have seen a lot of teams that have suffered. I am pleased with the performance and winning the game," added Arteta.
"We had to be really patient but have the intention to hurt them all the time and we did that."
The lack of a clinical striker has been pinpointed as the weakness in the Gunners' bid to beat Liverpool and Manchester City to the title.
For long spells it appeared the Arsenal could again rue the absence of a natural goalscorer as they struggled to make 80 percent possession count before half-time.
Jesus fired against the post with his first big chance early in the second half after an inviting flick from Martin Odegaard played him through.
But they finally got their reward as Forest switched off from Oleksandr Zinchenko's throw-in.
Jesus burrowed his way down the by-line but his effort should have been stopped at his near post by Turner.
Forest were architects of their own downfall again seven minutes later as Gonzalo Montiel's stray pass straight into the path of Odegaard sprang Arsenal on the break.
Odegaard picked out Jesus, who crossed for Saka to take a touch before firing in his 10th goal of the season.
Arsenal were cruising to victory as Forest had barely offered a threat all game until Awoniyi outmuscled William Saliba and fired home from close range in the 89th minute.
Awoniyi was then denied a dramatic equaliser deep into stoppage time by David Raya after Arsenal failed to clear a corner.
The Nigerian's return for the first time since November offers his side hope in their battle to survive.
But defeat leaves Forest perilously placed just two points above the relegation zone and with the threat of a points penalty hanging over the club after admitting to breaches of the Premier League's financial rules last season.
