Naismith handed the home side the lead after 14 minutes, smartly converting the rebound after Romelu Lukaku's close-range effort was kept out by goalkeeper Wojciech Szczesny.
Lukaku scored his fourth goal from his last six appearances after 34 minutes, collecting the ball from Kevin Mirallas outside the 18-yard box and taking on the Gunners defence before firing past Szczesny into the bottom left corner.
Everton's third goal came just after the hour mark as Mikel Arteta turned the ball into his own net as he attempted to stop Mirallas from having an easy tap-in.
Man of the match Naismith told Sky Sports 1: "We played very well. We then let them settle and get a lot of possession.
"Throughout the match, I thought we got the better of possession, starting all the way from the back. James (McCarthy) and Gaz (Gareth Barry) in centre-mid dictated play quite a lot and they created many chances, so it worked well."
Naismith has made just eight league starts and 17 substitute appearances this season, but has scored four goals and every one has been in an Everton victory.
In 34 appearances last season he scored only four goals in total and in 29 games in all competitions this campaign he has seven, but it is all-round influence which has been impressive.
Roberto Martinez made a couple of changes, putting Lukaku out on the right, with Naismith playing a more central role and the Scot said it was a success.
He added: "It worked very well, we've worked on it this week.
"It was more about trying to occupy the Arsenal defence and I thought Rom and Kev led by example doing that. They created space for me in the middle to link up and make runs through and I think for Kev's goal (the Arteta own goal) it worked perfectly.
"Kev's got on the ball and played me through and he's managed to get on the end it."
The win moved Everton to within a point of their fourth-placed opponents with a game in hand, leaving their chances for Champions League qualification in their own hands.
Victory was a significant boost for Everton, having drawn 1-1 at the Emirates Stadium in the league back in December before losing an FA Cup quarter-final 4-1 there last month.
And Naismith believes finishing in the top four would mean the world to the club and their fans but they must take it one game at a time, starting with next weekend's clash at Sunderland.
He said: "It would mean everything.
"We've believed from the start of the season and it just shows in these performances so we just need to concentrate on next week and hopefully get the points in."
Goalkeeper Tim Howard echoed his team-mate's confidence of a top-four end to the season and said: "We have to believe that (we'll finish top four) as we run out of games. We'd like to think we can."
The American was pleased with his side's performance and delighted to give the home support a great show against the Londoners.
He said: "That was certainly one of our signature performances since I've been here at Everton.
"The way we controlled the game, scored the goals and kept it clean at the back - I thought it was a brilliant performance.
"They were up for it. They know what it meant coming to the game and if we could take three points then we'd be hot on their (Arsenal's) tails.
"They've waited all season for a blockbuster performance like this and they'll feel like this was definitely the one."