Coutinho's passing was pin-point and Sturridge's finishing first-class as the Reds' ran riot at St James' Park.
And David Moyes will look to nullify their influence as he aims to win his first Anfield derby, according to Rush.
"Everton will be thinking that if they let Coutinho and Sturridge play, they will be in trouble," he told Liverpoolfc.com.
"Newcastle let the pair play last week, but they won't get that sort of space against Everton.
"I'm sure Moyes and Everton will be keen to get tight on them, especially Coutinho. But good players will come out on top.
"I think Sturridge will know what to expect as he's been in the English league for a long time and he's in form at the moment.
"We've also got the likes of Steven Gerrard and Jamie Carragher, who will tell them that this is no ordinary game. This is a game where you are going to get kicked, it's going to be hard work and you're not going to get a lot of space."
A win against the Blues would close the gap between the two clubs to just two points and hand Brendan Rodgers's side an outside chance of finishing above their rivals, who currently sit sixth in the Barclays Premier League table.
Rush continued: "I think it's incredibly important that we get the win. Everton finished above us last season and this year we have to better that.
"But even if we beat them on Sunday, there's no certainty that we are going to finish above them.
"It's going to be a fantastic game. We're playing at home but I don't think that makes much difference - I think Everton might even be favourites for the game.
"They go into the game knowing a draw would suit them because it would mean that we would not close the gap, in terms of finishing higher in the league."
The game will be Jamie Carragher's final Merseyside derby - and Rush insists the Bootle Boy will be as eager as ever to leave the pitch having downed the Reds' rivals from across Stanley Park.
"You'll miss people like Carra in the dressing room and you'll miss him in games like this," he said.
"During matches against Manchester United and Everton, the likes of Carragher and Gerrard will be telling the players that these are no ordinary games.
"Against Everton, they'll tell them, 'This is the Merseyside derby. This is the fans' game.'
"Carra will be letting the players know that they can't lose. He will be sorely missed once he leaves."
Earlier this week a panel made up of LFC TV staff decided that Rush was Liverpool's ultimate Merseyside derby hero.
The Welshman fired an astonishing 25 goals against our neighbours during a 15-year reign of terror and Rush explained how confidence would course through his veins whenever he caught sight of Everton blue.
"It's incredible how you feel," he admitted. "I wasn't going into games against them thinking I was going to score; I was going in knowing I was going to score.
"Everyone is going to get chances in the game and it's just whether you take them.
"It was different for me when I played against Manchester United. It took a while before I scored against them. I was going into those games thinking I might score. With Everton it was different.
"And that was all down to confidence. So after that 6-0 win against Newcastle, I'm sure that our players will be confident going into the game against Everton."