The former Juventus man has, unsurprisingly, taken the top flight by storm since moving to Abu Dhabi in July - leading the league's goalscoring charts going into Tuesday's clash.
And Vucinic continued his impressive start to life in the Middle East with a demonstration of his quality against the division's bottom side.
The Montenegro international had his hat-trick wrapped up within the hour, before Jonathan Pitroipa added a fourth late on to keep Al Jazira a point off leaders Al Wahda.
It was Vucinic's third hat-trick for Al Jazira and ensures the hosts' winless start to the campaign continued at the Ittihad Kalba Club Stadium.
Al Jazira's win leaves the top three unchanged from the weekend with leaders Al Wahda and Al Shabab also picking up wins.
Amer Omar's early goal ensured maximum points for Al Wahda against Al Fujairah while Al Shabab were made to work hard for their 3-2 win over Emirates.
Henrique Luvannor opened the scoring in a five-goal thriller at the Emirates Club Stadium only for Alhasan Saleh and Luiz Henrique to put the home side on top before the hour.
However, Caio Junior's side ensured they kept pace with the league's pacesetters thanks to late goals from Carlos Villanueva and Azizbek Haydarov.
Mahmoud Khamis struck late on for Al Nasr to ensure three points in a 1-0 win against Al Dhafra while 10-man Al Wasl edged further clear of the bottom two.
Fabio Lima struck after 31 minutes against Al Sharjah before Abdalla Saleh was shown a second yellow card, although the 1-0 win proved enough to move Al Wasl three points clear of Ajman beneath them.
Denis Stracqualursi scored twice for Bani Yas in their 3-0 win over Ajman while 10-man Al Ahli shared the points in a 1-1 draw with Al Ain.
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