Marcelo Bielsa's side moved within three points of leader Everton thanks to Bamford's 19-minute treble in the second half at Villa Park on Saturday (AEDT).
Bamford had one goal in 27 Premier League appearances prior to this season, but he already has six in six games this term.
It is a sweet moment for the 27-year-old, who endured a long and winding road to the top featuring long-running criticism of his finishing.
Bamford had seven loan spells during his time as a Chelsea youth academy graduate before moving to Middlesbrough, then finally finding his feet under Bielsa's tutelage at Leeds.
Leeds's third league win since its promotion from the Championship was the perfect response after losing against Wolverhampton Wanderers on Tuesday (AEDT).
For Villa, its four-game winning run came to a halt as it missed the chance to start a season with five successive victories for the first time in its history.
Villa only escaped relegation on the final day of last season, so the first defeat could serve as a reality check for Dean Smith's team after its unexpectedly strong start.
Smith had told his players they would get "a bloody nose very quickly" if they rested on their laurels, but they did not heed the warning as Bamford delivered the knockout punches.
Leeds could have been ahead inside the first four minutes when Bamford headed just wide from Ezgjan Alioski's deep cross
Pascal Struijk was deputising for the injured Kalvin Phillips in Leeds' midfield, but after earning an early booking for chopping down Jack Grealish and escaping a red card moments later for another foul, he found himself hauled off by Bielsa after just 21 minutes.
Villa nearly took the lead against the run of play when Grealish saw his shot superbly cleared off the line by Luke Ayling's last-ditch intervention.
Grealish carried Villa's main threat and the winger's penalty appeal was rejected by VAR (video assistant referee) after he went down under minimal contact from Helder Costa.
Showcasing the skill that has prompted many to question England manager Gareth Southgate's decision not to use him more often, Grealish twisted past the Leeds defence with some nimble footwork before Illan Meslier smothered his shot.
But Bamford broke the deadlock in the 55th minute with a close-range finish after Villa keeper Emiliano Martinez pushed Rodrigo's effort into his path.
Trailing for the first time in nine league matches, Villa was finished off by Bamford in the 67th minute.
Smashing a blistering strike into the top corner from the edge of the area, Bamford gave Martinez no chance.
Bamford completed his hat-trick in the 75th minute when he took Costa's pass and worked a yard of space inside the area before curling his shot past Martinez.