Scott Parker made it three promotions with three different clubs in the space of six seasons as Burnley extended their unbeaten league run to a club-record 31 games, bouncing straight back to the Premier League just as they did after their last two relegations in 2015 and 2022.
Brownhill poked the Clarets in front after Josh Cullen’s 28th-minute shot was saved.
There would not be a Burnley clean sheet to equal Port Vale’s all-time record of 30 in a single season as Tom Cannon quickly replied for the Blades, but Brownhill had the hosts back in front from the penalty spot before half-time, the midfielder’s 16th goal of the season.
Victory keeps Burnley level with Leeds at the top of the table, both with a chance to finish on…