Sunderland inches closer to safety
Stephane Sessegnon's strike in first-half injury time secured a second successive win for the Black Cats and their first over Everton in 20 attempts in all competitions.
But more importantly, it was well deserved as they dominated for long periods and limited the Champions League-chasing Toffees to a handful of half-chances in front of a delighted crowd of 44,614.
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 at the other end as Everton struggled to impose themselves in the face of a concerted assault by a Sunderland side rejuvenated by their new manager.
They ran out still basking in the euphoria of last weekend's famous derby victory at Newcastle, but under no illusions as to the task still ahead of them.
Di Canio had insisted within minutes of the final whistle at St James' Park that his team had taken only a small step forward, and with only those three points separating the Black Cats from the bottom three before kick-off, there was much work to be done.
In addition, a run of 19 games without a victory against Everton, 16 of them in the league did not augur well. But buoyed by their heroics on Tyneside, the Black Cats turned in a fine first-half display and ended it deservedly leading by the only goal, even if they did have to wait until stoppage time to secure their advantage.
They might have been ahead with just five minutes gone when Danny Graham, still awaiting his first goal in a red and white shirt, ran on to Larsson's header over the top, but initially hampered by team-mate Sessegnon, he fired straight at Howard.
Sunderland were a team transformed as Graham and Sessegnon caused problems up front for the visitors and a rearguard well marshalled by skipper John O'Shea allowed the Toffees few sights of goal at the other end.
Everton managed to work their way into the game after a tepid start, but managed only one attempt of note with O'Shea deflecting Kevin Mirallas' 33rd-minute effort behind for a corner.
By contrast, Sunderland threatened at regular intervals, most notably through Sweden international Larsson. He 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 they fell behind with Larsson turning provider with a pass which allowed Sessegnon to set himself before drilling a low shot past Howard, who got a hand to the ball, but could not prevent it from creeping inside the post.
Striker Nikica Jelavic replaced midfielder Darron Gibson at the break as Everton manager David Moyes looked for fresh impetus, but it was the home side who came close to extending their lead seven minutes after the break when full-back Danny Rose burst forward and powered his way past Leon Osman before blasting a left-foot shot wide.
Victor Anichebe had a chance to level seconds later, but he shot weakly straight at keeper Mignolet under pressure from Carlos Cuellar. But it was Sunderland who continued to press with the greater urgency as the second half unfolded, and Sylvain Distin and John Heitinga were repeatedly at full stretch to keep them at bay.
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. Anichebe fired over two minutes later with the Toffees enjoying their best spell of the game, and Mirallas drifted a 70th-minute cross dangerously towards the back post, but could not pick out a team-mate.
Moyes replaced Osman and Anichebe with Ross Barkley and Steven Naismith, but it was Larsson who almost handed the visitors a way back into the game. Mignolet had little choice but to catch his overhit back-pass as it sailed over his head, and referee Phil Dowd awarded an indirect free-kick and booked the Belgian.
Jelavic tapped the ball to Pienaar, who stopped it for Baines to smash 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, and Everton were appealing in vain for a penalty seconds later after Jelavic went to ground softly in a tussle with Rose.
The Associated Press was used in this report.