After a score-less first half, The Gers edged ahead on 60 minutes through Neil McCann while the visitors were reduced to ten man after Sean Kilgannon was shown the red card for violent conduct.
Michael Mols grabbed a second on 81 minutes and two minutes later Shota Arveladze wrapped up the win.
Dundee had to withstand a gritty fightback to claim local honours in the Tayside derby against Dundee United.
A first half double from Fabian Caballero followed by a Jonay Hernandez Santos goal - his first for the club - ten minutes into the second half had Dundee cruising.
Jim Hamilton and Jim McIntyre set up a tense finish but The Tangerines were unable to plunder an equaliser.
Hibernian ensured Motherwell remain firmly rooted to the foot of the table with a 3-1 success at Easter Road in a stormy encounter.
'Well took the lead through Steve Ferguson just after half-time but the visitors then had Daniel Sengewald sent for a second bookable offence.
Mixu Paatelainen quickly levelled matters before Tom McManus put Hibs in front on 64 minutes.
In the closing moments, Hibs had Grant Brebner dismissed and he was followed down the tunnel by Motherwell's Stephen Pearson and David Partridge before John O'Neil scored from the penalty spot.
Hearts stay ahead of their Edinburgh rivals on goal difference courtesy of Mark de Vries's first goal in six league games at Kilmarnock.
Partick Thistle picked up a much-needed three points at home to Aberdeen through goals from David Lilley (32) and Martin Hardie (79). Leon Mike scored a consolation for The Dons.
Click on the links below for an individual match summary:
Dundee 3-2 Dundee Utd
Hibernian 3-1 Motherwell
Kilmarnock 0-1 Hearts
Partick 2-1 Aberdeen
Rangers 3-0 Dunfermline
Click here for SPL table
