Striker Sam Vokes fired the Clarets ahead in the 28th minute from the penalty spot following a handball from Gonzalo Jara.
And, despite an equaliser from Simon Cox three minutes before half-time, Sean Dyche's side held on to top spot in the Championship ahead of Leicester on goal difference.
Forest, who remain in fifth place in the table, finished the game with 10 men after skipper Chris Cohen limped off with an injury.
Burnley had arrived at the City Ground amid their best run of form in 15 seasons and, despite seeing Forest make the brighter start, the Clarets looked like extending that when they took the lead from the penalty spot.
Jara had dangled a hand to block Kieran Trippier's cross giving Vokes the opportunity to convert, emphatically, from the penalty spot. The goal had come slightly against the run of play, with Forest having previously taken the game to their table-topping visitors.
Henri Lansbury, who had been harshly booked for a tackle on Michael Kightly, almost had a more positive impact moments later when Forest won a free-kick of their own on the edge of the box, with the former Arsenal man seeing a curling shot bounce back off the bar.
Cox had also spurned a good opportunity, flicking a header over the bar following a driving run and cross from the left from skipper Chris Cohen.
The striker was also denied by Tom Heaton when he did rather better with another opportunity, with Cox firing a shot across the face of goal which the keeper did well to push away.
And Forest did level in the 42nd minute when the lively figure of Jamie Paterson carved out the room to deliver from the opposite flank. The quality of his chipped ball to the far post was sufficient to leave Cox with a simple headed finish from close range.
Forest almost shot themselves in the foot at the start of the second period following a mix up between Hobbs and Cohen, which allowed Ings to surge into the penalty area.
Fortunately for the home side, substitute Nathaniel Chalobah made a vital lunging block to send Scott Arfield's resulting shot spinning wide.
Forest were showing attacking ambition themselves amid a closely-fought contest, with Majewski testing Heaton's reactions with a driven bouncing shot from just inside the box.
While the home side were again in the ascendancy Burnley still had menace, with Ings seeing a low shot deflected wide and Arfield forcing a fine block from Darlow with a rasping shot.