Two goals from the unlikely source of Ian Maatsen put the Clarets in control within 22 minutes, before Oliver Cooper halved the deficit before the half-hour mark.
However, Vincent Kompany's side held on for all three points, posting a sixth successive win in the second tier and to open up a 14-point lead over third-placed Blackburn Rovers.
Meanwhile, Middlesbrough now sit in fifth position courtesy of a 3-1 triumph at Birmingham City, the seventh success in 10 games under Michael Carrick.
After a goalless first half, two goals from Matt Crooks put Boro in control and although Tahith Chong kept Blues in the game in the final quarter, Chuba Akpom's 13th goal of the campaign secured another impressive win for the North-East outfit.
Middlesbrough had been on course to occupy fourth spot until Vakoun Issouf Bayo netted a late winner for Watford in their tussle with Norwich City at Carrow Road.
The Canaries have been overtaken by West Bromwich Albion, who rise to ninth after Daryl Dike netted the only goal of the game against Reading at The Hawthorns.
At the bottom end of the table, Kolo Toure witnessed his Wigan Athletic side suffer a fourth successive defeat, this one coming by a 4-1 scoreline to relegation rivals Hull City.
Nathan Broadhead cancelled out a Jacob Greaves opener to leave the game level heading into the final 15 minutes, but a Oscar Estupinan effort and two Tyler Smith goals earned a Hull a win which sees moves them seven points clear of the bottom three.
In the last of six 3pm kickoffs, a 93rd-minute goal from Ched Evans earned Preston North End a 1-0 win at Stoke City, who are managed by their former boss Alex Neil.