Alexis Sanchez's first goal for Arsenal since his £35m move from Barcelona claimed the prize of a place in the Champions League group stage for the 17th successive season on a tense night at Emirates Stadium.
The Chilean struck the goal that edged out Besiktas but Arsenal had to survive nervous moments – including playing the last 14 minutes with 10 men after Mathieu Debuchy was sent off – before winning this qualifier.
And for manager Arsene Wenger, Sanchez's strike ensured a rich reward on his expensive summer investment as Arsenal once again go into Thursday's draw for the group phase.
Besiktas were furious when Jack Wilshere's first-half tackle on Ramon Motta in the area went unpunished while Arsenal missed chances of their own to ease the anxiety sweeping around the stadium in the closing stages.
Former Arsenal defender Martin Keown on BBC Radio 5 live
"As an Arsenal fan, my heart was in my mouth a few times. The Jack Wilshere penalty claim was 100% a penalty for Besiktas.
"They have scrapped through, but they are through, and Arsene Wenger has preserved his wonderful record."
With Aaron Ramsey suspended, Wilshere was at the heart of Arsenal's best work with an energetic display that put recent poor form behind him, while Sanchez demonstrated the work-rate and quality up front that has Wenger believing he will be central to their season.
Arsenal also showed defensive resilience with reduced numbers in the dying moments as Turkish side Besiktas cast caution aside in the search for the goal that would have put them into the lucrative next stage of the Champions League.
It was always going to be tense after a goalless first leg and even though this qualifier was decided on fine margins, Arsenal will ultimately have no complaints because this was all about ensuring they did not slip out at this hurdle.
Wenger must now decide whether losing striker Olivier Giroud – out for the rest of the year after surgery on a broken tibia – will force him into the transfer market before the window closes on Monday.
Arsenal have attacking talent but it remains open to debate whether they have the sort of wider firepower that will enable them to mount a serious Premier League title challenge and tackle the best the Champions League has to offer.
Who Arsenal could get in the group stages
Best case: Arsenal, Basle, Sporting, Maribor
Worst case: Arsenal, PSG, Ajax, Roma
A promising early opening, which saw Wilshere slide an angled drive wide when he should have hit the target and Santi Cazorla do the same from keeper Tolga Zengin's wayward clearance, proved something of a false dawn.
Besiktas were determined in defence and carried a threat going forward that led to an air of frustration as their first half progressed.
And the visitors were also nursing a sense of injustice as they felt they were denied two penalties when Debuchy slid in on Mustafa Pektemek and when Wilshere appeared to take down Motta as he slipped making a challenge in the area.
Besiktas coach Slaven Bilic – forced to watch from the stands after being sent from his technical area in the first leg – certainly felt aggrieved as he jumped out of his seat in protest at referee Pedro Proenca's refusal to rule in favour of his side.
Just as Arsenal looked certain to get to half-time on level terms, Wilshere forced the issue with another run into the area to play in Sanchez for an angled finish.
The pair linked up again early in the second half as Wilshere's vision gave Sanchez another opportunity inside the area but his snapshot was deflected off target.
Former Chelsea striker Demba Ba gave Arsenal a worrying moment with a shot into the sidenetting on the turn – but the Gunners had moments of their own to settle it, with Debuchy heading wide and Alex Oxlade-Chamberlain seeing a shot blocked by Zengin from only eight yards.
The concerns increased for Arsenal and Wenger when they were reduced to 10 men with 14 minutes left after Debuchy received a second yellow card for tangling with Pektemek. He clearly got the ball but referee Proenca felt he had dragged the player back first.
Besiktas attempted to press home their numerical advantage, Ba almost getting on the end of one cross, but Arsenal held out and the Emirates was able to look forward to more Champions League football.