Burnley claimed a massive three points in their quest to stay clear of the Premier League relegation zone with a 2-1 win at Everton which at the same time put a dent in the host's top-four aspirations.
Dominic Calvert-Lewin's header before half-time gave Everton every chance to turn the game around, but they made little impact after the break as Burnley defended well.
Burnley are 15th with 33 points, seven ahead of Fulham who are in action later on Saturday at home to runaway leaders Manchester City.
They have now won at both Liverpool and Everton this season and another couple of wins should mean they are safe after they suffered a torrid start to the season.
"After seven games we had two points. Now we have healthy points return," Dyche said. "The players attitude has been magnificent. I think we've been performing pretty decently. There have been a lot of challenges this season, but the lads are alive and there have been good signs.
"Tonight I thought it was a real reward for what I believe is a good outfit."
It got even better for Burnley nine minutes later when McNeil, who was involved in his side's opener, produced a strike of stunning quality to double the lead.
McNeil jinked inside Everton midfielder Allan, then opened his body and bent an inch-perfect left footer that gave Pickford no chance as it found the top corner.
Burnley were rampant and almost made it 3-0 minutes later when Johann Berg Gudmundsson curled a low shot against the foot of the post, Pickford injuring himself as he flung himself full length to try and save it.
When Calvert-Lewin was left unmarked to head in a Tom Davies cross in the 32nd minute it looked as though Everton might still gain the win that would have taken them into fifth spot.
Pickford had to be replaced just before halftime with Joao Virginia taking his place for his Premier League debut.
Compared to the rip-roaring first half, the second period was more sedate which suited Burnley who managed to keep Everton away from the danger zone for the most part.
It was actually Burnley who went closest after that with Ben Mee heading against the woodwork.
The defeat was a bitter pill to swallow for Everton manager Carlo Ancelotti, whose side's home form has been a liability.
"A big disappointment, we lost a big opportunity to climb the table," the Italian said. "We made the same mistake we made in most games this season at Goodison (Park), we didn't start well."