© PA Photos
Stuart Armstrong gave the visitors a lead early on, but Efe Ambrose equalised for the league leaders just one minute later, before braces from Kris Commons and Anthony Stokes plus a goal from Joe Ledley allowed Celtic to inflict the crushing defeat.
Motherwell leapfrogged their opponents into second place in the table, beating Inverness Caledonian Thistle 3-0. Two goals from Michael Higdon and one from Nicky Law leave Motherwell 18 points off the top of the table.
Ross County also made progress up the table after securing all three points against St Johnstone. An 11th-minute goal from Ivan Sproule was enough to give the home side the win, moving County up to eighth.
Hibernian moved into the top four after securing a win at St Mirren. Leigh Griffiths scored from the penalty spot in the second half to secure the points after Jim Goodwin had brought Matt Done down in the box.
Results in full: Celtic 6-2 Dundee United, Hearts 0-3 Kilmarnock, Motherwell 3-0 Inverness, Ross County 1-0 St Johnstone, St Mirren 0-1 Hibernian