The Dutch champions thrashed Os Leoes in the curtain-raiser, while their visitors fell to a defeat at the hands of group favourites Borussia Dortmund.
Ajax kicked off the group stage with a tricky test away at Portuguese champions Sporting Lisbon, and two Sebastian Haller goals inside the first 10 minutes put them in a dominant position, before Steven Berghuis restored their two-goal lead soon after Paulinho's goal for the hosts.
Haller went on to find the net twice more in the second half, taking his tally to four for the game and earning his side an eye-catching 5-1 victory.
Erik ten Hag's side come into Tuesday's game in a fine run of form, having won their last six games in all competitions, scoring 29 goals in that time while Paulinho's consolation for Sporting Lisbon is the only one that they have shipped at the other end.
Following the dominant victory in Portugal, de Godenzonen thrashed newly-promoted Cambuur 9-0 in Eredivisie action, as Jurrien Timber, Berghuis, Noussair Mazraoui, Dusan Tadic, Mohamed Daramy, Haller and Danilo all got on the scoresheet alongside a David Neres double.
They have since built on that with two more victories heading into Tuesday, as they defeated Fortuna Sittard and Groningen 5-0 and 3-0 respectively to take their points tally to 19 points from seven top-flight outings.
Ten Hag's men will now look to add a second group victory to further strengthen their bid to reach this year's knockout stage, after their memorable run to the semi-finals in the 2018-19 season.
They meet a Besiktas side who will aim to bounce back from a defeat to Borussia Dortmund in the opening match.
The Black Eagles welcomed BVB to Istanbul, and goals from Jude Bellingham and Erling Braut Haaland saw the visitors take a 2-0 lead into the break, before Francisco Montero hit what would be a consolation goal for his side in the 94th minute.
While they bounced back with a 3-2 league win over Antalyaspor, as they came from two goals down in the second half, Sergen Yalcin's men have collected just one point from their last two league games.
The defending champions led 3-0 against Adana Demirspor, but an eye-catching comeback from the visitors saw Britt Assombalonga level the game in the 97th minute after goals from Matias Vargas and Mario Balotelli.
Last time out, Yalcin's men were handed a shock defeat by Altay, as Daouda Bamba hit an 88th-minute winner to snatch all three points, and they will now be desperate to bounce back in style with what would be an impressive victory in the Netherlands.
Sebastian Haller will lead the line with plenty of confidence, having hit four goals in his first Champions League appearance to take his tally to 22 goals, alongside nine assists, in 32 appearances since arriving in Amsterdam from West Ham United.
Besiktas have an unenviable injury list to deal with, as Umut Meras, Ajdin Hasic, Mehmet Topal, Georges-Kevin N'Koudou and Necip Uysal are expected to miss out alongside experienced defender Domagoj Vida and key attackers Michy Batshuayi and Alex Teixeira.
Midfielder Miralem Pjanic, who recently arrived on loan from Barcelona, was forced off with a knock in the first half last time out and is unlikely to make the starting XI on Tuesday.
Ajax possible starting lineup:
Pasveer; Mazraoui, Timber, Martinez, Blind; Gravenberch, Alvarez; Anthony, Berghuis, Tadic; Haller
Besiktas possible starting lineup:
Destanoglu; Rosier, Welinton, Montero, Yilmaz; Hutchinson, Josef; Ghezzal, Ozyakup, Larin; Karaman
We say: Ajax 3-0 Besiktas
While their recent form sees Besiktas already arrive in Amsterdam as major underdogs, their extensive injury list only compounds their problems, and we see the Black Eagles being comfortably defeated.
Ajax have been in fine form this season, and should overrun a depleted Besiktas side on home turf, given their impressive attacking ranks.
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