City stormed into a 3-0 lead in the first six minutes and by half-time had made it five without reply to set a new Premier League record for an interval lead by a team away from home.
Emmanuel Adebayor was on the mark twice and Craig Bellamy, Carlos Tevez and Patrick Vieira scored one each in the opening 45 minute romp which set up the win in atrocious conditions.
Vincent Kompany made it six after the break before Steven Fletcher pulled back the merest of consolations for beleagured Burnley with 19 minutes to go.
The Clarets, with just one win to their credit since their only away point of the season in drawing 3-3 at City in early November, brought full-back Danny Fox, midfielder Chris Eagles and striker Robbie Blake back into the starting line-up.
Roberto Mancini's men welcomed back Gareth Barry and Craig Bellamy as they looked to strengthen their bid for fourth place by making the most of a defeat earlier in the day for rivals Tottenham at Sunderland.
Adebayor was the first on the mark in the third minute with a shot from 12-yards out following a corner and two minutes later Bellamy raced through and slotted beyond Brian Jensen with an effort from just inside the penalty area after collecting Tevez's pass.
It was 3-0 moments later as a shot from Adebayor was parried by Jensen, leaving Tevez with the easy chance to tap home from close-range.
Before the game was 20 minutes old, it was 4-0 as Patrick Vieira headed firmly in from 12-yards following a corner from the left by Adam Johnson.
That prompted large numbers of Burnley supporters to leave the ground, disgusted at the severe added blow to their side's hopes of pulling clear of the bottom three.
Blake, Fletcher and Graham Alexander all shot wide for Burnley while their best chance of the half was a header from David Nugent saved on the line by Shay Given.
But City were firmly in control to say the least and a minute after Tevez had had a shot come cannoning back off a post, Adebayor made it five just before the break whe he was left clear by a pass from Tevez and made no mistake.
Burnley's David Nugent had the first chance of the second-half when he shot just wide after working his way into a good position on the edge of the penalty area.
But on 57 minutes, it was six to City as Kompany headed in another corner from Johnson.
The rain which had been falling, often very heavily, for much of the game was making life difficult for the players but referee Alan Wiley and fourth official Kevin Friend resisted calls from the Burnley bench for the match to be abandoned.
On 71 minutes, Fletcher pulled one back for Burnley when he picked up substitute Wade Elliott's ball to fire beyond the advancing Shay Given in the Citizens' goal.