However, despite the long sought after victory which seemed so often as though it would never come, there is still much for Everton to improve on if they are to pull clear of the relegation battle.
Goals are still at a premium.
Dominic Calvert-Lewin's strike just before half-time following an odd and unlikely rebound off Burnley's unlucky goalkeeper, proved enough in the end to secure all three points for the Toffees.
It was his second goal in consecutive Premier League games after a drought of nineteen matches, but he was also guilty of missing several other great chances to add another and give the Blues some room to breathe.
And his second half replacement Beto - who should in my view have been starting alongside him - also had opportunities to score and a good claim for a free-kick that was waved away.
So, while one goal was sufficient to beat a team as poor in front of goal as Everton are and one that has only managed to find the net thirty-two times, it won't be against higher scoring sides.
Although they have some eminently winnable games remaining, all of the Toffees upcoming opponents (apart form Sheffield United in the penultimate match) have scored more than the Blues.
Therefore, as I have said repeatedly, Dyche cannot continue to just keep it tight and hope for a single goal to win the three or four games he needs to effectively ensure survival.
That is also because as we all know Everton are still facing a potential points deduction of unknown proportions when the Premier League's commission reports again on the club's alleged second PSR breach.
This decision could be made as early as next week and might mean the Toffees have another two or three points deducted.
So once again it is imperative that the manager finds a a way to infuse his team with more attacking threat.
Dyche continues to put his faith in ageing players like Ashley Young who offer nothing going forward while sticking doggedly to his 4-4-1-1 formation.
While there might be a case for continuing with this approach away from home at places like Chelsea, when Everton are at home Dyche must take a more positive attitude.
As I have said umpteenth times, the manager should give Beto a start alongside Calvert-Lewin and also give more opportunity to attacking talents like Nathan Patterson and Youssef Chermiti.
Andre Gomes must keep getting game-time.
I have previously been an advocate of using Abdoulaye Doucoure in that deep lying role behind the centre-forward, as Dyche has done most of this season.
But Doucoure has been a shadow of his earlier self this season ever since he returned from those hamstring injuries he first suffered in December.
Meanwhile, Andre Gomes has returned to the Everton side after a long absence following a loan spell in France and then injury.
He has proved to be the one genuinely creative player in midfield that the Blues have and he had a solid game overall on Saturday.
With Doucoure struggling I think Gomes represents a good alternative and should get as much opportunity as possible to help influence games and provide a genuine creative outlet, which Everton otherwise lack.
Midfield is a mess.
In a wider sense the Toffees midfield as a whole is unsettled and uncertain and this is having a negative impact on the team's performances.
To be fair, there have been a lot of injuries particularly affecting the Blues engine room but I think Dyche needs to find a settled and balanced midfield for the remaining games of the season.
For me he only needs one defensive player in the middle of the pitch and that player should be Amadou Onana.
Alongside him should be a more progressive, attacking partner like Gomes, assuming he is fit and more genuine width and pace either side of the central midfielders.
This width, such as could be provided by Patterson or Arnaut Danjuma when he is fit, would give the greater dynamism and attacking threat that is desperately needed.