After winning their Ladbrokes Premiership opener, Hibs have taken just one point from their last four league games to tumble down the table.
Hearts are also badly out of form and sit bottom of the league with just two points from their first five games, causing the pressure to mount on boss Craig Levein.
Long-serving full-back Stevenson, who has played in 40 Edinburgh derbies during his Hibs career, knows the impact a victory in this fixture can have.
The 31-year-old sees Sunday's clash at Easter Road as the perfect opportunity to put things right after a poor run of results.
He said: "In recent years there has been a good buzz about the place and a positive mentality going into these games. It's obviously been a bit different recently.
"We want to right a few wrongs and there is no better way of doing that than winning the derby.
"We need to step up as players because from Monday to Friday we're doing everything right, we're working on everything, we've got our game plan.
"And when it comes to the game, it's not working and that's to do with us.
"So we need to step up now. We needed to step up five or six weeks ago but this is when you make your name as a Hibs player - in derbies - and hopefully this can kick-start our season.
"We need to be ruthless, with the ball and without the ball.
"If that's steaming into a tackle then so be it, if that's being clinical in front of goal or a block in your own penalty box - these are the small margins that can win games and we need to be ruthless on the day."
Stevenson is expecting a close game and is focused only on getting the right result rather than worrying about the performance.
"If you can get your head right in these games then the rest takes care of itself," he added.
"I don't think anyone's going to blow anyone away, it's going to be tight, probably one or two goals in it. You need to stay in the game.
"I don't care how badly we play as long as we get a win on Sunday."