The Toffees have claimed four victories in their last five Premier League matches to stay in contention for a UEFA Champions League spot.
They sit three points off the pace at present, but could close that gap with a win at third-placed Arsenal on Tuesday night.
Everton's record against the Gunners is not the best - with David Moyes having collected just two points in north London during his 11 years in charge - but Jagielka is looking for them to prove that they can raise their game when it matters most.
The England international said: "Unfortunately, we haven't turned up in some really big games. That's the challenge for us now and there is only one way to change that.
"We'd like nothing better than to put in a fantastic performance at the Emirates, come away with three points and lay that to rest. But it is not always as easy as that.
"We have gone to the Emirates and not got the rub of the green a few times.
"Maybe we have under-performed away, but we have done very well at home against them. We'd like to turn the tide as soon as possible."