Goals from Ian Black, Bilel Mohsni and Dean Shiels gave Ally McCoist's side all three points at Ibrox as they extended their advantage over Dunfermline at the top of the table.
The Light Blues are now just four fixtures away from going through the 36-game campaign without losing, with home ties against Ayr United and Stranraer coming after this weekend's trip to Stenhousemuir before they round off the season at East End Park.
It was another below par performance from McCoist's side but they almost got the perfect start as Black saw his sweetly-struck drive from the edge of the area was tipped over by keeper Darren Hill with just three minutes on the clock.
Despite having little zip or energy about their play, Rangers should have had the points wrapped up fairly early on. Like on Saturday against Dundee United, however, poor finishing would infuriate the Light Blue legions.
Striker Jon Daly was the main culprit as he headed wide from a corner, sclaffed another effort by when in a promising position and then missed the target with only the keeper to beat after he collected a sliderule pass from midfielder Nicky Law.
Shortly after the break, Stevie Smith came close with a long-free kick before Daly glanced a header just wide after he connected with a Richard Foster cross.
The champions finally made the breakthrough after 67 minutes and it was to prove well worth waiting for as Black smashed a terrific shot from fully 30 yards into the top corner of Baxter's goal.
It didn't take long for McCoist's side to add to their tally and clinch the win, Mohsni converting after Dean Shiels' cross clipped the bar and fell to the defender at the back post.
With just a couple of minutes remaining, Shiels got his name on the scoresheet as he headed home Fraser Aird's cross to wrap up a deserved win for the champions.