Bury were hit for six as they put on a horror show at the Ricoh Arena.
Chris Stokes, Baily Cargill and James Maddison gave Coventry a dream start as they raced into an early 3-0 lead.
John Fleck added a fourth on the stroke of half-time before Adam Armstrong netted two in as many second-half minutes to wrap up the three points and pile the pressure on manager David Flitcroft whose side have managed only two wins in their last 12 matches.
Flitcroft made three changes from the 3-0 defeat to Barnsley. Tom Pope was absent from the squad and Peter Clarke and Danny Pugh dropped to the bench.
Right-back Joe Riley returned for his first start in over a month, while Andrew Tutte and Kelvin Etuhu provided a welcome boost in central midfield as the manager shifted to a 4-5-1 formation.
Adam Armstrong almost gave the hosts a dream start when he raced through on goal inside three minutes but Ian Lawlor made a fine save to turn the ball around the post.
But from the resulting Joe Cole corner Cargill was left completely unmarked and volleyed the ball past the helpless Lawlor.
Former England international Cole registered his second assist of the game nine minutes later when Cargill turned his deep free-kick over the line.
Set-pieces were again Bury's undoing on the 16th minute when a short free-kick was played to Maddison in the middle of the Shakers half and he drilled the ball into the bottom right-hand corner.
Maddison came a whisker away from netting his second in as many minutes when he floated a free-kick narrowly over the crossbar.
Flitcroft had seen enough and brought on substitute Ryan Lowe for Etuhu as he switched to a 4-4-2 formation.
The change gave Bury a short confidence boost as Andrew Tutte got on the end of a fine move but his shot was palmed away by the sprawling Reice Charles-Cook.
Jacob Murphy fizzed a low shot across Lawlor's goal on the 34th minute before Leon Clarke was denied by a stunning Charles-Cook save at the other end.
Out of nothing Fleck fired in a fourth from 35-yards out after picking up the ball, turning and rifling a shot into the bottom corner on the stroke of half-time.
The woeful defending forced Flitcroft into making his final two substitutes at the break. Reece Brown and Chris Hussey were withdrawn as Peter Clarke and Pugh slotted into the back four.
Two minutes after the restart Leon Clarke spurred a glorious opportunity volleying over from six yards out.
Coventry were in cruise control with Cole rolling back the years and dictating the game. Bury failed to get near the attacking-midfielder and he fed Armstrong on the 69th minute and the forward duly slotted it past Lawlor.
The on-loan Newcastle forward bagged his second in as many minutes when the defence parted and he strolled through and shot straight through the body of Lawlor who should have done better.
The hosts toyed with the visitors late on, stroking the ball around the pitch at their own leisure until the clock ticked to 90 and the Shakers were sent packing back to Greater Manchester red-faced and humiliated.