The Benin international's strike in first-half injury time secured a second successive win for the Black Cats and their first over Champions-League chasing Everton in 20 attempts in all competitions.
Midfielder Sebastian Larsson had earlier gone close with three free-kicks, the last of which Tim Howard had to claw out of his top corner.
However, opposite number Simon Mignolet had little to do as Everton struggled to impose themselves in the face of a concerted assault by a Sunderland side rejuvenated by their new manager.
Sunderland might have been ahead after five minutes when Danny Graham ran on to Larsson's header over the top but fired straight at Howard.
Larsson then clipped the bar with a 12th-minute free-kick and whistled another just wide five minutes before the break before forcing a fine save with a third dead ball effort in the final minute of the half.
Everton were still re-grouping after that near miss when Larsson fed Sessegnon who drilled a low shot past Howard.
Half-time substitute Nikica Jelavic glanced a 61st-minute header wide from a Leighton Baines cross and just could not react in time after Mignolet spilled Marouane Fellaini's snapshot.
The hitherto excellent Larsson almost undid his good work with an overhit back pass. Mignolet had little choice but to catch it as it sailed over his head and referee Phil Dowd awarded an indirect free-kick and booked the Belgian. Baines smashed it towards goal but a solid wall of defenders did its job.
Adam Johnson should have cemented the victory with six minutes remaining but saw his shot blocked by Howard's legs.