Second-placed Rangers' 10 point penalty for going into administration, and subsequent 1-0 loss at home to Kilmarnock on Saturday, had left Celtic in a strong position even before they kicked-off at Easter Road.
But Gary Hooper's double, as well as goals from Antony Stokes, Charlie Mulgrew and substitute Ki Sung-Yueng saw Celtic pile on the agony for both arch-rivals Rangers and, indeed, second-bottom Hibernian.
Stokes headed Celtic into a 14th minute lead against his former club when he was first to Mulgrew's inswinging cross.
And six minutes later Celtic were 2-0 in front when, after Stokes had beaten three defenders, the unmarked Hooper scored the first of his two goals.
The second half was only two minutes old when Mulgrew added a third goal, with a curling free-kick from more than 20 yards out.
Another long range shot, this time from Hooper, bounced over goalkeeper Graham Stack's arms to make it 4-0 before Kris Commons's drive deflected off fellow substitute Ki to complete the scoring 13 minutes from time.
Earlier, St Johnstone missed the chance to go fourth after sharing the points in a goalless draw away to Aberdeen at Pittodrie in Sunday's other Scottish top-flight match.
Source: AFP
Source: AFP