Ricky Sbragia arrived on Merseyside with an 18-month contract in his back pocket and his team full of confidence after emphatic victories over Hull and West Brom in recent weeks, as well as a deserved point collected against Blackburn on Boxing Day which kept them well clear of the drop zone.
Everton had also succeeded in picking up points despite having all their senior strikers absent during the busy Christmas programme.
David Moyes, though, was desperate to give the Goodison Park faithful something to cheer today with the Blues having the poorest home record in the Premier League before kick-off.
The Toffees welcomed back Leon Osman from injury to make his 150th career appearance with young Gosling making way, while influential Sunderland pair Teemu Tainio and Kieran Richardson returned to give the Black Cats a timely boost.
It was Sunderland who started the brighter with Richardson and Daryl Murphy linking well and their team-mates harrying and forcing the home side into simple errors.
However it was Everton who struck first in the ninth minute with a stunning Arteta free-kick after Osman had been felled 20 yards from goal by Richardson.
The Spaniard struck the ball with venom through the wall and past Martin Fulop's flapping arms to a roar from the home fans.
A minute later Tim Cahill could have doubled the lead but shot wide from close range, while at the other end Danny Collins sent his header over Tim Howard's crossbar after rising well to meet a corner kick.
The game evened out thereafter until the 25th minute when Steven Pienaar was toppled on the edge of the Sunderland area.
That man Arteta stepped up again but took a different route to goal. He blasted the ball into the wall and as it rebounded back to him, he caught it sweetly on the volley, firing into the back of Fulop's net via a deflection off Tainio's shin.
Cahill missed a sitter two minutes later as he headed wide from six yards out and unchallenged as Everton began to display their superiority.
However, the second half never really got going until the 83rd minute when substitute Gosling, making only his second appearance in a blue shirt, tapped in Everton's third from a Joleon Lescott cross, following more good work from Arteta.
Everton handed a debut to youngster Lukas Jutkiewicz in the closing stages and the lanky forward looked promising.
Unfortunately for the Black Cats they could only bring on the likes of Dwight Yorke and David Healy who, realistically, were not the men to change Sunderland's fortunes.
Phil Neville went agonisingly close with a fierce 30-yard strike soon after as Everton turned on the style in the last few minutes, but in fairness the 3-0 score belied a rather laboured afternoon for both teams.