The Turkish midfielder's goal on 65 minutes proved decisive in a game the hosts shaded but were made to pay after missing vital opportunities
In what turned out to be a low-key friendly despite both teams fielding reasonably strong teams, the hosts had the better of the game but were taught an important lesson in taking your chances when they present themselves by the Dutch champions.
Nigel Adkins lined up his side in a 4-3-3 formation, with Brazilian Guly do Prado and new signing Jay Rodriguez supporting Rickie Lambert in attack.
Southampton made by far the brighter start and the first chance of the game arrived when Lambert showed good strength in the box and teed up Adam Lallana, but the young midfielder failed to get good contact on his shot.
Many home fans thought their side was ahead moments later. Guly’s pass found Rodriguez, who put the ball in the net only to find he had been flagged offside by the linesman.
Lambert fired wide from distance and then away goalkeeper Kenneth Vermeer was forced into action. The 26-year-old shot stopper did well to block an effort from James Ward-Prowse after good work from Lallana out wide.
On 35 minutes, Ajax had their first attempt when captain Siem De Jong did well to find space, but then fired poorly over the crossbar from outside the box.
Attentions were turning to half-time when Lambert again threatened at the other end. A trademark powerful shot from the striker deflected off defender Toby Alderweireld and only just off target.
The second half was certainly a lot quieter than the first as the visitors tightened up defensively, but Lambert again worked Vermeer with a header from Lallana’s whipped corner.
Ajax were starting to get a strangehold on the game, though, despite creating many clear-cut opportunities.
On 65 minutes, they moved ahead when Ozbiliz drove inside from the left wing and fired a shot past Kelvin Davis and into the far corner.
Adkins reacted with a triple substitution and it almost immediately paid dividends with 20 minutes left when Morgan Schneiderlin found one of the players who had been brought on, Billy Sharp, but the striker took too long to get his shot away in what was a clear opening.
Ajax ensured that was the last clear chance they conceded and professionally closed out the closing stages - which were fragmented by a number of substitutions - looking more comfortable as the game went on, leaving the hosts to rue their earlier missed opportunities.
The Saints still have three more pre-season matches – against Wolves, Bristol City and Udinese - before they kick-off their league season with a daunting away trip to champions Manchester City.