The Gunners head to Goodison Park on the back of five straight Barclays Premier League wins which have catapulted them up into the top four.
Indeed, should results go their way this week, then the Gunners could even be third heading into the next round of fixtures.
Van Persie, though, knows nothing less than 100% commitment will produce the result needed at Goodison - where rivals Tottenham, Chelsea and Manchester City have all been beaten this year.
"It is tough to play the way we all want. We need to be consistent and get a win over the line, like at Liverpool," Van Persie told Arsenal Player.
"We did it now, and we can enjoy it, but we need to show it again (at Everton) and it may even be a harder game, but we have to give it our maximum and see where it ends."
Arsenal have come from behind to win in four of their five victories, the latest with a dramatic stoppage-time winner from Thomas Vermaelen to beat Newcastle 2-1 at the Emirates Stadium.
Van Persie added: "If you look at the last couple of weeks, we showed we have a lot of character in our side, and we can be proud of that.
"Now we need to show that over a period of a whole year. We need to have a run like that for months and even win the ugly games.
"We showed signs that we can do it because against Liverpool we didn't play well, but still nicked it.
"We came from behind in the past four games and ended up winning the game. That shows we can do it, not only once or twice or three times, but lots of times. So why not show it 20 times or whenever it is needed?"
Gunners boss Arsene Wenger revealed there were no fresh injury concerns from the Newcastle game, with the extra time off because of no Premier League match last weekend allowing Vermaelen to recover from a knock to his ankle.
Full-back Kieran Gibbs has just returned from a lay-off and believes having the likes of Andre Santos and Carl Jenkinson now fit again in reserve can make a big difference over the run-in.
He said: "We should have players coming back from injury now so we should be getting some fresh legs looking to go for the rest of the season strongly.
"It is a relief to have a break until the next game and it was important for us to get that because we have played quite a lot recently in a short space of time."
Gibbs maintained Arsenal now do not know when they are beaten.
He added: "In previous seasons you wouldn't have thought we would have the strength to come back, but now we don't really think about the score, we just keep playing," he said.
"The team is showing great character at the minute and we need to keep that going.
"Football changes so much. We have seen over the last few seasons that anything can happen now and it is important for us to cement our place (in the top four) and keep winning."
Wenger, meanwhile, remains cautiously optimistic on the recovery of England midfielder Jack Wilshere, who has not played yet this season because of an ankle problem.
"It is difficult to set a deadline on Jack. We go week by week with him, but his last scan was very good so we don't have worry any more," the Arsenal boss said.
"It is about progress and fitness, however I can't set a date."
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