Michel was appointed in June after leaving Girona, with whom he was relegated from LaLiga.
With the returning Daley Blind as the only new face in Ajax's starting XI, the Amsterdam outfit started on the front foot through veteran Davy Klaassen, who stood on the receiving end of an inviting Kasper Dolberg cross. Klaassen hit goalkeeper Dragan Rosic with his volley, but tapped in the rebound to get Ajax in front after three minutes.
Ajax didn't stop the pressure then and there, with Dolberg, Oscar Gloukh, and Youri Regeer testing Rosic several times in the opening 20 minutes.
Despite being overrun in the opening phases, Vojvodina responded aptly through Petar Sukacev's classy header in the 28th minute.
The game remained one-way traffic despite the level scoreline, which was quickly toppled again by the visitors when Steven Berghuis fired the ball in past Rosic's near post after Mika Godts' corner sailed to the back of the penalty area.
Ajax were in control and further extended their lead shortly after half-time - Mika Godts played around with three Vojvodina players before serving Oscar Gloukh in the box, and the midfielder hammered it past Rosic for the 3-1 after 52 minutes.
Michel's men treated the final 30 minutes as a fitness test, controlling possession and letting Vojvodina barely get the opportunity to form a threat.
Ajax's evening was given the cherry on top when 16-year-old debutant Mohamed Abdalla scored his first goal for Ajax, tapping the ball underneath Rosic after a delightful assist from fellow youngster Abdellah Ouazane.
Ajax take a 4-1 lead home to Amsterdam, where they'll host Vojvodina for the away leg on Thursday, July 30th, in a sold-out Johan Cruyff ArenA.