Two goals in the last 17 minutes from Callum Wilson – the opener his 50th in the Premier League – saw the Magpies register their first points of 2021.
It was Newcastle's first victory at Goodison Park since 2010 and their first league double over the Toffees since the late Sir Bobby Robson was in charge in the 2001-02 season.
"It is something we have been working on now for weeks," he said.
"We (previously) sat deep and played on the counter-attack and we have been working on getting on the front foot and I think the players have enjoyed it.
"Certainly looking at their performance today they have enjoyed it and they enjoyed the change – but you need results to go with it.
"We've had an awful eight weeks with illness and injury and you're always hoping you can get the squad fit and healthy.
"We have got our big players on the pitch and had a really good bench to pick from too, which is important."
The biggest performance of the afternoon came from Bruce's key player Wilson, who was a threat all game.
"He has put in a big performance. You need your big players and we need a bit of service to him," added Bruce.
"Of course he will get the headlines but for me a clean sheet is always a great start.
"All-round we were at it today. I thought we thoroughly deserved it and to win so convincingly was pleasing."
Everton boss Carlo Ancelotti cut a frustrated figure in his post-match press conference.
The defeat meant the Toffees have taken just one point from games against Leicester and the Magpies, which Ancelotti said were crucial to the bearing of the rest of the season.
He criticised the "lazy" performance but was at a loss to explain why.
He said: "I think they (Newcastle) won the game because they showed more fighting spirit on the pitch, more concentration, more motivation and I think they were the weapons we had when we won games.
"I think we forgot all this today at home. I don't know why. That was the reason, it was not a tactical or physical reason. It was a mental reason. The psychological aspect affected our performance.
"We were lazy, slow, not focused, we gave 12 corners to them, a lot of thrown-ins.
"We didn't win duels, second balls. This is the game, not only the quality (on the pitch).
"You can show your quality if you are there in this game. The game is always to win duels, to win second balls. We were not on the pitch today."
"They are talking at this moment. I was not involved in this because I was involved in the game," the Italian added.
"In the next days they can find a solution to leave. I don't know which clubs."