Pearson prodded home three minutes before half-time to cap an impressive performance just 24 hours after joining the club on loan from Championship rivals Derby.
Ross Wallace gave the visitors brief parity moments after the break at Ashton Gate on Saturday, sending a looping volley past David James in the City goal, but Eddie Howe's team were level for less than 15 minutes.
Brett Pitman popped off the bench to slot home Pearson's cross to restore the Robins' advantage and Albert Adomah galloped clear of the visiting defence to beat Clarets stopper Lee Grant and seal three crucial points in style.
Burnley striker Jay Rodriguez fired an early shot wide of James' near post before the front man was denied by the former England stopper with a neat low save after a through-ball from Charlie Austin.
City responded quickly and on-loan midfielder Pearson was within inches of finding Nicky Maynard in front of goal as the match livened up after a tentative first quarter-hour.
In a frantic phase of play, home winger Adomah saw his effort blocked en route to goal by Burnley's Brian Easton before Austin went close for the visitors.
But City were establishing control on the game, and visiting keeper Grant had to be alert just after the half-hour to prevent Adomah's snap-shot from sneaking past him and into the back of the net.
And Grant seemed to be keeping Burnley in the match single-handedly in the lead-up to the interval.
The keeper produced saves from Pearson and Marvin Elliott to stop the Robins taking the lead, while Yannick Bolasie fired over the crossbar as the home side huffed and puffed furiously without reward.
Austin handed the Clarets momentary respite at the other end of the pitch, but the former Swindon striker could not direct his right-footed attempt from the edge of the area on target.
Three minutes before the break, City got the goal their dominance of territory and possession deserved. Elliott's misdirected header fell to the feet of debutant Pearson, who bundled the ball into the net to hand the hosts the half-time lead.
Burnley responded in the best possible way less than two minutes after the interval.
Junior Stanislas stood a chipped cross up into the Robins' penalty area, and Wallace was on hand to fire a looping volley past James and level affairs at Ashton Gate.
But City manager Derek McInnes' has instilled a renewed sense of self-belief among his squad, and the home side rallied to retake the lead just after the hour.
Pearson, at the heart of everything positive, centred for Pitman who made no mistake in converting the chance for his first goal in his last six appearances.
And the hosts put the game to bed nine minutes later when Neil Kilkenny fed Adomah through a gaping hole in the Burnley backline, and the Ghanaian ran from halfway before shooting emphatically past Grant.