Everton started the brighter of the two sides in Paolo Di Canio's first home match, forcing four corners in the first few minutes, with Marouane Fellaini looking dangerous from the set-piece delivery.
However, it was Sunderland who had the first clear-cut chance. After John Heitinga dallied, hoping that Tim Howard would come out to claim the ball, Danny Graham had a snapshot which the American got down well to save.
The half then became something of a battle between Seb Larsson and Howard. Too often Everton gave away free-kicks around their area, and the Swede clipped the crossbar after 12 minutes.
There was a talking point on 20 minutes, as James McClean and Kevin Mirallas tangled in the Everton half. McClean appeared to kick out at the Belgian, but referee Phil Dowd saw fit to only give a stern reprimand and not brandish a card.
Five minutes before the break Larsson again fired just wide from a set-piece with Howard beaten, but just before half-time he forced the American into a clawing save to keep the score at 0-0.
Less than a minute later and Everton were architects of their own downfall. Howard rolled the ball out to Leighton Baines, and the England international inexplicably gave the ball away. Sessegnon took advantage instantly, toe-poking the ball into the bottom left hand corner.
Everton started the second half brightly, but again lacked energy as they made little inroad into Sunderland's defence, and it was Sunderland who had the next chance, the excellent Danny Rose marauding forward before firing wide.
It took an hour for Simon Mignolet to be forced into a save, a Fellaini shot rebounding of Nikita Jelavic and into the arms of the goalkeeper. Two minutes later, and Victor Anichebe shot over.
With 12 minutes to go, Everton almost got level in bizarre fashion. An overhit backpass caught Mignolet off his line, and the goalkeeper was forced to pedal back and catch the ball, booked for his troubles in handling the ball. Baines' free kick could only hit the wall.
In the last ten minutes Sunderland inevitably dropped deep, but in truth Everton failed to put on enough pressure to merit an equaliser. The only shot on target in the latter stages fell to Adam Johnson, who forced Howard into a low save with his feet.
Jelavic went over in the box to claim for a penalty in injury time, but there was to be no stopping Di Canio's celebrations at the final whistle.