Defender Mohamed Ahmad put Al Ain in front two minutes into the quarter-final, getting on to the end of a cross from Rayan Yaslem and scoring from close range.
The UAE champions went 2-0 up in the 16th minute through a Hussein Elshahat strike into the bottom right corner from inside the box and midfielder Bandar al-Ahbabi scored a close-range goal in the 60th minute for 3-0.
Al Ain will play South American champions River Plate of Argentina in Tuesday's semi-final.
"It's a great pleasure to play the winners of the Copa Libertadores... we will try and make it difficult for River," said Al Ain coach Zoran Mamic.
Esperance controlled possession for most of the game but struggled to take advantage, managing just one shot on target in 18 attempts.
The Tunisian side's coach Mouine Chaabani said he was disappointed with his team's performance, telling reporters they had lost their focus after the first goal.
"All the players were thinking individually, not collectively," he said.
Al Ain, who qualified as champions of the host nation and played in front of 21,333 spectators at their home Hazza Bin Zayed Stadium, piled on the pressure whenever they had the ball.
Al Ain's Caio missed an opportunity to get on the score sheet in the 58th minute with a wayward shot from the left-hand side of the box but made amends moment later with an assist to Ahbabi who struck the third goal.
"When the team is focused on the game like today the result is coming from this discipline, from this concentration... this focus. I'm very, very proud of my team," Mamic said.
In rare scenes for a UAE soccer match, flares were briefly lit in a section of the stadium where Esperance fans were seated shortly after the Tunisian side went 3-0 down.
Japan's Kashima Antlers came from behind to beat Mexico’s Chivas Guadalajara 3-2 in Saturday's earlier game, earning a place in Wednesday semi-final against European champions Real Madrid.
(Reporting by Alexander Cornwell; editing by Clare Fallon)
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