The Croatian arrived at Goodison Park almost exactly a year ago - signing from Rangers for £5m - and quickly became a hit with fans by racking up 11 goals in the latter stages of last season.
Jelavic, 27, has been less prolific in recent weeks having failed to find the net in his last seven Premier League outings - but Moyes is adamant he trusts the player to rediscover his goalscoring form.
Talking in the wake of the 2-1 FA Cup fourth-round victory over Bolton at the weekend, the Scot said: "I want to give him every opportunity to get it right and I felt this was an opportunity.
"I have been looking at it and I will need to look at it again. Obviously I want to give him every positive I can to show I trust him by playing him in the team."
The Toffees are yet to add to their squad in the January transfer window, but Moyes admitted he remains hopeful of bolstering his options in attack.
He added: "I would love to (bring another striker in) but I would be very surprised if I did."