The Staggies showed no sign of rustiness as a double from Ross Stewart and goals from Josh Mullin and Billy Mckay proved too much for the Angus side to overcome.
Ross County took the lead after just seven minutes through a counter attack.
Jamie Lindsay picked up the ball in his own half and pushed forward, skipping past a couple of opposition players into space.
He gave the ball to Mullin on his left, whose shot with the outside of his right boot flew into the top corner, curling away from Montrose stopper Aaron Lennox.
The Premiership newcomers would double their lead in the 14th minute.
Summer signing Joe Chalmers played a simple ball to Stewart in the middle of the part, and the towering striker charged forward into the Montrose box.
He was forced slightly wide by his marker, but Stewart still managed to get a shot away and found the bottom corner.
County dominated the ball for the rest of the first half, but Josh Skelly forced Ross Laidlaw into action twice before the interval to show that the visitors were not down and out just yet.
The hosts all but sealed the win right after half-time, though, when Mullin sent in a deep cross to find Stewart unmarked at the back post to head into the bottom corner.
But Montrose continued to show signs of life when Matty Allan stole the ball from Chalmers inside the County box in the 51st minute, with his shot deflecting off Liam Fontaine and into the net.
County took control from there, dominating the ball without really threatening goal, before Mckay rounded off the win in the 85th minute with a cool chip over the onrushing Lennox.