If this is what Mikel Arteta’s vision for Arsenal looks like, then the future is in very safe hands. First-half goals from the youth team products Bukayo Saka and Eddie Nketiah secured a first away victory for their manager since he succeeded Unai Emery and set up another trip to the south coast to play Portsmouth in the fifth round.

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Along with the impressive Joe Willock and Gabriel Martinelli, Arteta’s decision to field a starting lineup that featured four players aged 20 or under paid dividends here with an all-action display which left Eddie Howe’s side chasing shadows at times during the first half.

Despite a frenetic finish that saw the Bournemouth substitute Sam Surridge pull one back, Arsenal held on for a deserved victory that clearly delighted Arteta. “We played a really young squad because I wanted to see the reaction,” he said. “I’m very pleased because I saw a lot of things that I really liked. They have courage to make big decisions and they were terrific. That’s the difference with these kids.”

Arteta won this competition with Arsenal twice as a player in 2014 and 2015 and had stressed the importance of using it as a springboard for the future before this tie. Perhaps with that in mind, he handed 20-year-old Nketiah his first start since his return from a loan spell with Leeds alongside the teenager Martinelli and the record signing Nicolas Pépé in attack, while Matteo Guendouzi and Willock were recalled in midfield. The late comeback against Chelsea last week after David Luiz’s red card in the first half offered proof of Arsenal’s growing team spirit under their new manager and that was very much in evidence in the opening exchanges here.

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Saka has been pressed into emergency cover at left-back in recent weeks but the way he took his opportunity in the fifth minute suggests he could make an unfamiliar position his own. A driving run from Willock created the chance, with Martinelli’s perfect touch allowing Saka to hammer the ball past Mark Travers at his near post. Bournemouth’s usual approach to the FA Cup since they reached the Premier League means they have reached the fifth round only once in the last five seasons, although on this occasion Howe fielded several of his first-choice side.

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Yet despite the confidence-boosting victory here over Brighton in midweek which lifted spirits as they battle against relegation, the hosts struggled to find a foothold against Arsenal’s energetic young side.

Willock could have doubled their lead in the 20th minute had he directed his shot either side of Travers before the midfielder’s excellent pass found Saka in acres of space on the left flank to supply a perfect cross that was tapped home by Nketiah. In response, Harry Wilson saw his effort parried away by Emiliano Martínez and Daniel Gosling then somehow failed to hit the target with a free header five minutes before the break.

Arsenal’s defence, featuring Sokratis Papastathopoulos and the error-prone Shkodran Mustafi seemed to be standing firm – a relief for Arteta after a move for the Flamengo defender Pablo Mari reportedly hit the skids over the £7.5m proposed fee earlier in the day. A small pocket of visiting supporters even started chanting Mustafi’s name just before the whistle blew for half-time.

Facebook Twitter Pinterest Bukayo Saka opens the scoring after five minutes with a crisp strike that went in off the bar. Photograph: James Marsh/BPI/Shutterstock

Having seen his side totally outplayed, Howe sent his players out early for the second half and they responded with a vastly improved performance that finally applied some pressure on Arsenal’s defence.

Mustafi was fortunate to get away with one lapse in which he collided with Martínez as he chased back, with the defender then having to leave the field on a stretcher after a long delay that resulted in eight minutes of stoppage time. Arteta later revealed Mustafi will have a scan this week on a suspected ankle injury that could yet force his hand in the transfer market. Jack Simpson almost gave Bournemouth hope soon after when his header from a corner whistled just past the post with Martínez stranded.

The Arsenal manager then threw on Dani Ceballos for his first appearance since November in the week he insisted the Real Madrid loanee remains part of his plans. The 23-year-old could yet end up playing a more important role but was largely confined to defensive action here as Bournemouth turned to their top scorer, Callum Wilson, in a desperate attempt to force a replay. Their breakthrough finally came when Surridge latched on to a cross from his fellow substitute Simon Francis but it proved nothing more than a consolation in the end. “We really struggled to deal with Arsenal in the opening half-hour but, once we recovered, it was too late,” admitted Howe, who will now turn his attention to Saturday’s Premier League meeting with their fellow strugglers Aston Villa.