Lille made a promising start to the match, but it was Everton who created the first opening when Steven Pienaar linked up with Samuel Eto'o, who lost control as he threatened to pull the trigger inside the box.
However, the hosts continued to look threatening going forward, and were inches away from breaking the deadlock from an Idrissa Gueye strike which drifted just wide of the post.
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In a tight first half which contained very few goalscoring opportunities, the uncharacteristically quiet Aiden McGeady tried his luck with a half-volley which failed to provide a tough challenge for Lille goalkeeper Vincent Enyeama.
Divock Origi looked lively throughout the first half for the hosts, and he came close to opening the scoring after the break with a powerful strike which sailed wide from the edge of the box.
The introduction of Romelu Lukaku after the hour mark almost had an immediate impact as the Belgian released McGeady, whose low effort was blocked by Enyeama.
Both sides continued to search for a breakthrough in the closing stages, but the defenders at each end would dominate for long spells as promising attacks regularly broke down in the final third of the pitch.
However, there was still time for a late scare for Lille as Eto'o threatened to snatch the win for his side by curling wide from the edge of the box after beating a couple of defenders.