Houssine Rahimi scored twice to put the former champions in command of the tie before his elder brother Soufiane hit their team's third and Giorgos Giakoumakis scored their fourth in the 85th minute.
"We knew it was going to be tough, we had to give it our all and I think we did that," said Giakoumakis.
"We were really mature from the first to the last moment and we managed to score a good amount of goals and have a good victory."
Al Ain went in front in the 25th minute when Houssine Rahimi pounced on Saad Al-Nasser's under-hit back-pass to slot through Nawaf Al-Aqidi's legs and he doubled the lead when he side-footed home from eight yards in the 63rd minute.
Soufiane Rahimi added the third when he judged his run onto Alejandro Romero's through ball into the penalty area to perfection, remaining onside to drive his first-time shot into the bottom corner.
Giakoumakis netted the fourth as Rahimi turned provider, rolling the ball into the path of the Greek forward 15 yards from goal and he gleefully converted.
Al Hilal registered a 2-1 win over Qatar's Al Gharafa in their league phase opener with a goal in each half from Ruben Neves and Sergej Milinkovic-Savic in Riyadh after both sides had been reduced to 10 men.
Crysencio Summerville was sent off after a 32nd-minute altercation with Abdulrahman Al-Rashidi and, following the resulting melee, Al Gharafa's Ismael Bennacer was also dismissed by referee Omar Al-Ali.
The four-time champions from Saudi Arabia went ahead three minutes into first-half stoppage time through Neves' penalty, with the spot-kick awarded when Al Rashidi hauled winger Saimon Bouabre down inside the area.
Milinkovic-Savic doubled Al Hilal's lead 17 minutes from time when his header was deflected past goalkeeper Ahmed Kone and that was to prove crucial as Alaa Eddin Hasan scored for the visitors from distance deep into stoppage time.
The first eight finishers in the expanded 16-team league phase will progress to the knockout rounds in March, with the quarter-finals, semi-finals and final to be played in Saudi Arabia in April and May.