Everton had failed to secure a victory throughout the whole of September, and after a frustratingly insipid draw against West Ham last weekend, they needed to end this current period of games with a win before another international break.
And while the result was a good one and maintained the Toffees' excellent record against the Eagles on Merseyside, something that has continued despite the move from Goodison Park, there are some key issues for David Moyes to try and iron out before Everton's next Premier League match at Manchester City.
Of course, the first is the one that has plagued so many Blues managers for so long now and continues to cause problems: the lack of goal-scoring threat from his strikers.
Thierno Barry started against Palace, and although the youngster tried hard, he seemed lost at times and lacking in sharpness. In truth, he looks way off the pace and under-cooked for the Premier League, and his first goal in royal blue seems a long way off.
Beto came on in the second half and provided a more direct and consistent threat, while it was his headed effort that led to Jack Grealish's winning goal in extra time.
However, other than Beto's solitary strike at Wolves, neither of these two forwards has looked at all likely to provide that much-needed goal threat up front.
I felt that when Everton decided to let Youseff Chermiti leave for Rangers on deadline day, the club should have had another striker lined up to replace him and offer both real competition and an alternative to Barry and Beto.
Obviously, the Blues did not bring anyone else in, and so it is down to those two to deliver the goals, which they are clearly struggling to do.
One other option discussed before is to switch tactics and try a different solution, such as moving another player into the striking role, whether that is Illman Ndiaye, perhaps, or Carlos Alcaraz.
Another attacking issue is the lack of contribution from the club's most expensive summer signing, Tyler Dibling. Like Barry, he failed to take his chance on Sunday and was also withdrawn at half-time.
After his breakout season last term with Southampton, it was hoped that the hugely talented 19-year-old could continue to add to his growing reputation.
So far, though, he has also found it tough to do so and has found it difficult to make a positive impression for his new team. Given how much money he cost, this is a slightly troubling situation.
It is early days in his Toffees career, and he has had little opportunity to play up to now, so hopefully he will find his feet again and start contributing substantially as well.
One other problem that has surfaced and was on display again against the South Londoners is this Everton side's recent run of wildly inconsistent performances during each half of a match.
As in the recent Merseyside derby defeat at Liverpool and at home playing West Ham, the Blues started slowly and lethargically against their visitors on Sunday and let Palace take almost complete control of the game. After taking a deserved lead, the Eagles should have been out of sight by half-time.
That their opponents were not was mainly down to another inspired effort in between the sticks from Jordan Pickford, who was certainly the better of the two England goalkeepers on the pitch.
Things improved after the break as Moyes made some necessary and effective changes, with Everton eventually hauling themselves back into the contest. The issue remains, though, and it will surely prove costly if it is not corrected.
So, with a break of two weeks before the next Premier League games, the manager has plenty to think about and resolve if Everton are to sustain and improve upon what has been a solid, if largely unspectacular, first two months of the season.