The Clarets, who have been unbeaten in the league since November, got off to the perfect start when Ashley Barnes redirected Josh Brownhill's low shot into the back of the net.
The home side equalised right after half-time when Championship top scorer Chuba Akpom scored from the spot after Josh Cullen felled Cameron Archer in the penalty area.
However, Burnley showed their quality and determination as Connor Roberts steered in the winner from Nathan Tella's near-post cross.
This secured Burnley's return to the top-flight with seven games to go in the Championship, and sparked wild celebrations on the pitch and among their travelling fans.
This promotion can be worth over £300 million ($372 million) over five seasons, if the club survives their first season in the Premier League, according to last year's Deloitte Annual Review of Football Finance.
Burnley will now look to secure the title, break the 100-point barrier and become the first team to go unbeaten at home in a Championship season since Newcastle United in 2009-10.
Given the amount of change that Vincent Kompany has overseen since taking charge, it was somewhat ironic that it was a combination of two players who were there when he took over that gave Burnley the lead.
Brownhill's low strike from the edge of the area might have been going in anyway but 33-year-old Barnes, who has now won promotion to the Premier League three times with the club, stuck out a foot to redirect it and leave Boro keeper Zack Steffen with no chance.
Tella missed a gilt-edged chance to double their lead before the break when he fired wide after being played in behind the home defence.
Barnes, who is leaving the Clarets in the summer after nine years, said it was “the end of an era” and it was “time for him to move on”.
The veteran forward’s role was crucial in the promotion campaign, and his parting gift to Burnley was a goal that could prove to be worth millions of pounds.
Burnley's next objective will be to win the Championship title. They are now 19 points clear of third-placed Luton Town with only six games remaining.
Sheffield United, who are in second place, are the last team to have beaten Burnley in a league game 19 matches ago. Burnley's last match of the season is against Sheffield United.