Al-Jazira looked to be on course for three points, with Ricardo Oliveira's 18th-minute strike separating the sides heading into injury time, before Humaid Abbas equalised.
Bruno Correa then completed the comeback in dramatic fashion for Al-Nasr, who finished 14 points behind league champions Al-Ain last season.
Al-Sha'ab began their campaign in spectacular style with a 4-0 victory over fellow promoted side Al-Ittihad Kalba.
Following a goalless first half, Rodrigo Vergilio's double (55 and 61) - the first from the penalty spot - put the visitors in control before late strikes from Rodrigo Silva (82) and Nasser Khamis (88) sealed an impressive triumph.
Issa Obaid's 22nd-minute strike set Al-Shabab on their way to a 2-0 win over Bani Yas.
Edgar Da Silva added a second 10 minutes from time to get Al-Shabab off to the right start.