James Vaughan claimed a 16th-minute opener for the Shakers before strike partner Tom Pope doubled their lead on 40 minutes.
Stuart Beavon pulled one back for rock-bottom Coventry with a 65th-minute header but despite some late pressure, the Sky Blues could not avoid a seventh defeat from nine in the league.
Bury, meanwhile, are now four points above the bottom four after taking 13 points from 15, with three straight wins since Lee Clark took charge.
Coventry keeper Lee Burge had to deny Paul Caddis and Vaughan before the latter showed neat footwork to beat two defenders and sidefoot into the bottom corner.
The visitors replied with Charles Vernam and Callum Reilly going close, before Pope latched onto a Callum Styles through-ball to slot home and double the home side's lead.
Burge made a point-blank save from Pope just after the break, but Reilly and Vernam both fired wide before Beavon gave the visitors a lifeline, scoring from a left-wing cross by half-time substitute Ryan Haynes.
Burge then kept out a Taylor Moore header but Bury keeper Joe Murphy pulled off two fine saves to deny Kevin Foley and Reilly an equaliser.
Report supplied by the Press Association.
Match ends, Bury 2, Coventry City 1.
Second Half ends, Bury 2, Coventry City 1.
Hand ball by Kwame Thomas (Coventry City).
Corner,  Bury. Conceded by Jordan Willis.
Tom Beadling (Bury) wins a free kick in the attacking half.
Foul by Kwame Thomas (Coventry City).
Substitution, Bury. Niall Maher replaces Callum Styles.
Attempt saved. Callum Reilly (Coventry City) right footed shot from the right side of the box is saved in the bottom right corner.
Corner,  Coventry City. Conceded by Leon Barnett.
Corner,  Coventry City. Conceded by Joe Murphy.
Attempt saved. Kevin Foley (Coventry City) right footed shot from outside the box is saved in the top right corner.
Substitution, Coventry City. Jodi Jones replaces Charles Vernam.
Corner,  Bury. Conceded by Jordan Willis.
Attempt blocked. Callum Styles (Bury) left footed shot from outside the box is blocked.
Attempt blocked. Jacob Mellis (Bury) right footed shot from the right side of the box is blocked.
Jacob Mellis (Bury) wins a free kick in the defensive half.
Foul by Nathan Clarke (Coventry City).
Callum Styles (Bury) wins a free kick on the left wing.
Foul by Dion Kelly-Evans (Coventry City).
Foul by Callum Styles (Bury).
Dion Kelly-Evans (Coventry City) wins a free kick in the defensive half.
Attempt missed. Charles Vernam (Coventry City) right footed shot from outside the box is close, but misses to the right.
Substitution, Bury. Hallam Hope replaces James Vaughan.
Dion Kelly-Evans (Coventry City) is shown the yellow card for a bad foul.
Foul by James Vaughan (Bury).
Kevin Foley (Coventry City) wins a free kick in the defensive half.
Attempt blocked. James Vaughan (Bury) left footed shot from the centre of the box is blocked.
James Vaughan (Bury) wins a free kick in the defensive half.
Foul by Callum Reilly (Coventry City).
Attempt saved. Taylor Moore (Bury) header from the right side of the six yard box is saved in the centre of the goal.
Goal!  Bury 2, Coventry City 1. Stuart Beavon (Coventry City) header from the centre of the box to the top left corner. Assisted by Ryan Haynes with a cross.
Corner,  Bury. Conceded by Kwame Thomas.
Corner,  Bury. Conceded by Jordan Willis.
Paul Caddis (Bury) wins a free kick in the defensive half.
Foul by Kwame Thomas (Coventry City).
Attempt saved. Stuart Beavon (Coventry City) header from the centre of the box is saved in the centre of the goal.
Substitution, Bury. George Miller replaces Tom Pope.
Attempt missed. Charles Vernam (Coventry City) left footed shot from outside the box is close, but misses to the right.
Attempt missed. Callum Reilly (Coventry City) right footed shot from the centre of the box misses to the left.
Attempt saved. Cameron Burgess (Bury) header from the centre of the box is saved in the top centre of the goal.
Resurgent Bury held on for a home win over Coventry to take another step away from the League One relegation zone.