Mourinho's men were guilty of missing a host of chances and were made to pay for their wastefulness when Steven Naismith grabbed the winner on the stroke of half-time to hand Roberto Martinez his first Premier League victory as Everton manager.
Debutant Samuel Eto'o and Andre Schurrle were particularly guilty of squandering good opportunities for the visitors in the first half, and Naismith pounced from Nikica Jelavic's header back across goal in first-half injury time.
Substitute Oscar felt he should have been awarded a penalty in the second half but referee Howard Webb waved away the protests.
Mourinho handed a first competitive start to transfer window signing Eto'o, with Fernando Torres dropping to the bench.
Everton gave a debut to Gareth Barry but fellow new boy James McCarthy had to settle for a place among the substitutes.
In a lively opening, Eto'o almost opened his Premier League account as early as the fourth minute - Ramires found space on the right and his pin-point cross was met by the Cameroonian who could only head over from eight yards.
At the other end, Jelavic was equally as wasteful. Ross Barkley won possession in midfield and he supplied Naismith, whose excellent cross was met by the Croatian but he headed tamely at Petr Cech.
Tim Howard was given a huge reprieve in the 29th minute after a small lull in clear-cut openings.
Howard's attempted pass out of defence was intercepted by Eden Hazard. He centred to Eto'o who looked destined to tap into the empty goal, only to be denied by a wonderful sliding interception from Barry.
Chelsea continued to press and Mourinho was visibly frustrated as two good opportunities were not converted. First, Ramires flicked a ball in the air and volleyed at goal only to be denied by Howard.
The Brazilian then broke free again and prodded into the path of Schurrle, but the German blasted well over when one-on-one with the goalkeeper.
And Chelsea were made to pay for their profligacy in front of goal when Naismith notched the opener on 45 minutes.
Barkley crossed to Jelavic at the back post and he headed back across goal to the Scot, who could not miss when heading home on the goal line.
The second half started in similar fashion with Chelsea creating but unable to break down Everton's resistance.
Schurrle broke free but chipped over Howard into the side netting before Howard parried a Hazard effort into the path of Eto'o, but he failed to connect as the ball went harmlessly wide.
Oscar replaced Juan Mata, and the Brazilian thought he should have had a penalty in the 58th minute.
He ran across Sylvain Distin and was felled in the box but Webb was unmoved. Replays suggested Oscar may have had legitimate claims for a spot-kick as he appeared to touch the ball before the Frenchman.
With 20 minutes remaining, the lively Ramires stretched for a Branislav Ivanovic cross but he could only fire into the side netting.
Everton looked threatening on the counter attack as Chelsea searched for the equaliser, and had a series of corners before Kevin Mirallas had an effort beaten away well by Cech.
The home fans thought their team had a late penalty when Seamus Coleman was brought down by Hazard, but the incident occurred just outside the box.
And they came desperately close to a second in the 88th minute when Leighton Baines saw his free-kick rebound off the crossbar.