The Staggies have now gone 32 games without defeat after Colin McMenamin netted his 17th goal of the season to ensure Derek Adams' side left Cappielow with just a point.
With just two games remaining, the Ton are six points ahead of ninth-placed Ayr United and virtually guaranteed their place in the First Division next term after a Marc Smyth strike gave them a share of the spoils against the champions.
The Cappielow boss said: "We gave away a poor goal through slack marking, but I felt we competed just as well as Ross County after that and probably had more of the possession.
"We've scored a good goal, and in the end we're a bit disappointed we didn't go on to win it."
The afternoon started badly for the home side as McMenamin headed home a Richard Brittain cross just six minutes into the game. But the hosts were soon level as striker Andy Jackson set up Smyth to net his first-ever goal for the Greenock club.
County goalkeeper Michael Fraser twice denied Archie Campbell in the closing stages to leave Moore frustrated.