The Croats are bottom on no points and can now only fight for third spot and a Europa League place with two games left.
A superb back-heel pass by Christian Eriksen played in Van der Wiel, who first searched for a team-mate before deciding to shoot and score the first on 20 minutes.
Siem de Jong set up Sulejmani five minutes later to double the lead and De Jong sealed victory 20 minutes into the second half. Nicolas Lodeiro grabbed a fourth in injury-time.
Ajax are second in Group D with seven points after four matches, three ahead of next opponents Olympique Lyon. A scoring draw in France on November 22 would send Frank de Boer's side through.
Group leaders Real Madrid qualified for the knockout stages by beating Lyon 2-0 away on Wednesday.
Ajax left their league woes of one win in six matches behind them in a confident display against the uninspired visitors.
"They surprised us a bit with their tactical plan but we regained control and kept them under pressure," De Boer told reporters.
The 4-0 scoreline also helped Ajax's goal difference compared to Lyon if the head-to-head between the sides does not come into play.
They drew 0-0 in Amsterdam in September.
"We know that a score draw will do in our next match at Lyon but we are not a team that just can lean back on the counter attack, so we will also try to play our own game in Lyon but with cleverness," the coach added.
