Jesus had the assistance of former Arsenal goalkeeper Matt Turner to break the deadlock as the American let the Brazilian’s shot from a narrow-angle slip through his legs.
Saka then rounded off a blistering counter-attack from the visitors and Taiwo Awoniyi’s late strike was too little, too late for the home side.
Mikel Arteta’s men had not won away from home since early December as their title challenge stumbled over the festive period.
But Arsenal kept the pressure up on Liverpool with the two sides set to face off at the Emirates on Sunday.
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.
The lack of a clinical striker has been pinpointed as the weakness in the Gunners’ bid for a first Premier League title in 20 years.
For long spells, it appeared that Arsenal could again rue the absence of a natural goalscorer as they struggled to make 80 per cent 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.
Turner then unconvincingly parried from Saka’s shot across goal as the Arsenal pressure built.
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 the architects of their 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.
AFP