Abdoulaye Doucoure and Dwight McNeil both scored braces to go with an own goal from Brighton goalkeeper Jason Steele as Everton profited from swift and incisive counter-attacks to secure three points that moved them out of the relegation zone.
To score five goals with 23 per cent of the possession is a reflection of how they allowed Brighton the ball in the match but were lethal once they won it off their hosts.
"They (Brighton) play a particular way with two boxes in midfield. I said to the lads it is about focus.
"Our tactical shape has been pretty good since I've come in here. But it's about focus when they change their tune and try and pop it around the corner and play neat and tidy," Dyche told BBC.
"But equally it's not just about shadow play, you've got to go and break it up and first half we did that so many times. Second half they had a good spell but we calmed that down and I thought we saw the game through very well."
Everton drew 2-2 at Leicester City in their previous game when they created more than enough chances to win, and Dyche believes they gained confidence from that result.
"A lot of people thought we were good at Leicester, we were very good and conceded soft goals. Tonight we got paid back for that performance because the energy was there, the tactical performance, but also the quality," he said.
Everton are two points clear of the relegation zone with a home game against Manchester City to come on Sunday.
After that, they travel to Wolverhampton Wanderers and host Bournemouth in their final game of the season.
"This is just another step as I said when we beat Arsenal, it's just one step," Dyche said.
"We'll see what happens over the next few games. The players have delivered. They deserve a lot of credit."
Leicester's relegation worries deepen
Willian and Tom Cairney both scored twice to help Fulham beat Leicester City 5-3 at home on Monday, ending the visitors' three-game unbeaten Premier League run and leaving them in the relegation zone after the day's other results.
Leicester, who had taken five points from their last three matches, have 30 points with three games left, falling to 18th place below Everton and Nottingham Forest who both won later in the day.
Fulham never really looked to be in danger with Leicester playing catch-up throughout the contest after a dismal first-half display, which was criticised by playmaker James Maddison.
"Big game for us and we were not at it. We were not hungry enough to want to win the game. We need to do the basics well," Maddison told the BBC.
"We can't defend like we did, that is why we are where we are but it not just the defence, it is the team. The team needs to be watertight and that comes from the front too.
"They played through us. They scored three goals in the first half and it left too much to do."
Leicester face Champions League-chasing Liverpool and Newcastle United in their next two games.
Marco Silva's Fulham have now won 14 league games this season - equalling a club record in the Premier League.
"Great moments of football, great goals. The way we played from the first minute was really good," Silva told the BBC.
"We prepared well for the game and the players executed the plan very well. We clearly deserved the three points and it should have been much more comfortable. That is something for us to work on and keep improving."
Fulham remain 10th in the table.
