Henrik Larsson sent the visitors on their way with the opener on 21 minutes with his 41st goal of the season.
Stilian Petrov put The Bhoys in total command with a quick-fire brace (29,32).
Alan Thompson added a fourth from the penalty spot on 59 minutes to wrap up the win.
Scott McNicol pulled one back for the hosts ten minutes but Martin O'Neill's men ran out winners to put the pressure on Rangers, who travel to Dundee on Sunday.
Motherwell remain bottom of the table after being held to a 2-2 draw with fellow strugglers Dundee United.
Stephen Pearson gave Motherwell the lead on 11 minutes, but Charlie Miller levelled things up four minutes after the restart.
Jim McIntyre fired United in front nine minutes from time, but Tony Vaughan earned the hosts a priceless point with an 85th minute equaliser.
Kilmarnock kept their European hopes alive with a 1-0 win over nine-man Hearts at Rugby Park.
Gary McSwegan netted the only goal of the game on 29 minutes as the visitors were reduced to nine men with Andy Webster and Austin McCann seeing red in the second half.
Hibernian recorded an impressive 3-1 win over Aberdeen at Easter Road.
Matthias Jack fired the home side in front three minutes before the break and a brace from Derek Riordan (61,72) ensured the win.
Fergus Tiernan grabbed a late consolation for The Dons two minutes from time.
Livingston moved further clear of trouble with a comfortable 3-1 over Partick.
Davide Xausa netted the opener for the hosts on 25 minutes and Rolando Zarate doubled the lead a minute before the break.
David Lilley pulled one back for the visitors on the stroke of half time, but Juanjo Camacho wrapped up the victory with the third five minutes after the restart.
Click on fixture for full match summary
Dunfermline 1-4 Celtic
Hibernian 3-1 Aberdeen
Kilmarnock 1-0 Hearts
Livingston 3-1 Partick
Motherwell 2-2 Dundee Utd
Click here for updated league table
