The substitute scored from close range after a free-kick broke kindly for him.
Darren Dods gave Forfar the lead after 19 minutes and Gavin Swankie almost added to it before the break when he lobbed Ryan Scully only for the ball bounce against the post.
Swankie had three chances on the counter-attack in the second half but could not put any of them away. However, just when it looked as if Forfar had done enough, Moore had the final say.
Stranraer moved within two points of the second-placed Fifers after a 2-1 win at Arbroath.
Jamie Longworth put Stranraer ahead after only three minutes with his 16th goal of the season. Steven Doris equalised a couple of minutes into the second half but Chris Aitken hit what proved to be the winner after 62 minutes.
East Fife eased their relegation worries with a 1-0 win over Stenhousemuir, with Gary Fisher scoring the only goal five minutes from half-time.
Brechin City's home match against Airdrieonians was postponed after a pitch inspection.