Mitch Megginson's sixth-minute opener was the perfect start for the table-toppers and Fraser Fyvie doubled their advantage just past the half-hour mark.
Craig Johnston pulled one back for Montrose before the break but Rangers held on to retain their five-point gap over Airdrieonians, who they face next week in a top of the table clash.
The Diamonds also enter that match on winning form and claimed an excellent victory with a 2-0 triumph over Queen's Park. Callum Smith broke the deadlock in the 38th minute and Dylan Easton wrapped up the scoring in the first minute of first-half stoppage time.
East Fife remain bottom after they were downed 2-0 by Clyde which kept the hosts in the hunt for a top-four finish.
Ally Love fired Clyde in front with 19 minutes played and Lewis Jamieson added a second prior to the hour mark.
Dumbarton only hold a three-point advantage over basement side East Fife following a 2-0 reverse at home to fifth-placed Falkirk.
Goals by Jaze Kabia and Charlie Telfer put Falkirk in control after 27 minutes and that was how it ended with Martin Rennie’s Bairns now three points outside the play-off positions with six games remaining.
Kevin Cawley grabbed the only goal of the game for Alloa Athletic to defeat Peterhead at home by a 1-0 score.
The visitors finished with 10-men after Andrew McDonald was shown a red card late on.