The Belgium international came off the bench in what could be his final Premier League appearance for the Blues with Real Madrid waiting but could not break the deadlock in a forgettable 0-0 draw.
With the Europa League final against Arsenal at the end of the month Hazard played just 22 minutes at the King Power Stadium.
Gonzalo Higuain missed a glorious first-half chance for Chelsea while Jamie Vardy and Youri Tielemans wasted Leicester's best openings as the Foxes finished ninth.
Tottenham's 2-2 draw with Everton secured third for Maurizio Sarri's side but they still finished a mammoth 26 points behind champions Manchester City.
The visitors should have gone ahead after just three minutes when Jorginho found an unmarked Ross Barkley but the midfielder could only blast straight at Kasper Schmeichel from six yards.
Chelsea were dominant with the Foxes suffering another slow start and Schmeichel got down to smother Willian's low effort after 15 minutes.
The hosts were searching for their first double against Chelsea since 2000-01 but there was little urgency from Leicester, even with a top half place at stake.
Ben Chilwell, James Maddison and Tielemans launched efforts for Leicester but the game struggled to shake its end-of-season feeling.
Scoreflashes from Brighton got the biggest reactions of the first half with eyes cast on the title race.
Vardy glanced a header from Chilwell's free-kick straight at Willy Caballero after 31 minutes before both sides blew excellent chances to open the scoring late in the half.
First, David Luiz's slip let Vardy through clear on the left but he opted to pass to Tielemans instead of shooting and his lay-off was woeful and the midfielder could only cut back to Caballero.
And in first-half injury time, the quiet Higuain should have scored but fluffed his lines terribly, firing wide from six yards after Cesar Azpilicueta's cross.
It was a golden chance and one which they never recreated even after bringing Hazard off the bench with 22 minutes left.
Before his introduction little had happened in a flat game which meant little.
Leicester title winners Danny Simpson and Shinji Okazaki got their farewell appearance before they leave in the summer and the hosts carried little threat.
Their haul of 16 points over the last eight games has only been bettered by Manchester City and Liverpool but they could not replicate that form.