Lewis Grabban’s first-half header was enough to give the hosts victory at Villa Park as Leeds fell to their 10th defeat of 2018.
Villa, who at the very least are guaranteed a play-off spot, have played one game more than second-placed Fulham, while Cardiff - a point better off than Steve Bruce’s side - have played two games fewer.
Heckingbottom suffered his seventh defeat in 13 games since taking over as Leeds manager, while Villa boss Steve Bruce extended his managerial record of never having been beaten at home by Leeds to eight games.
The hosts completely dominated the first period but had a more difficult job on their hands after the break when Leeds started to cause some problems.
Jack Grealish, who produced a fine performance against Cardiff on Tuesday, again provided some silky play as he tormented Leeds and played a leading role in Villa dominating for long spells of the first period.
Villa, buoyed by their success over promotion rivals Cardiff, mounted a relentless attack from the start and Leeds had to stage a rearguard action to keep on level terms.
Leeds appeared content to operate defensively and relied heavily on the impressive Paudie O’Connor, making only his third appearance, and Matthew Pennington to contain Villa’s free-flowing attack.
But the hosts broke the stalemate in the 29th minute through on-loan striker Grabban’s fifth goal for the club. Some slack defending from the visitors allowed Grabban to head in a seemingly harmless left-wing cross from Grealish.
In sharp contrast to their indifferent first half, Leeds were more positive in the second period and took advantage of some casual Villa play.
Northern Ireland international Stuart Dallas went close to an equaliser with a fine dipping shot while Ronaldo Vieira fired just over.
But Villa were still a threat and only a reflex point-blank save by Bailey Peacock-Farrell prevented Jonathan Kodjia - on his first home start of the season - opening his account in the 60th minute.
Kodija was withdrawn after 66 minutes on his return from injury and Villa saw out the remaining time to record a third straight home win.
Aston Villa: Johnstone, Elmohamady, Chester, Jedinak, N Taylor, Whelan, Snodgrass, Grealish, Onomah (Samba 85), Grabban (Hogan 78), Kodjia (Adomah 67). Unused substitutes: Lansbury, Hourihane, Bree, Bunn.
Leeds United: Peacock-Farrell, Dallas, O’Connor, Pennington, Pearce, Alioski (Grot 66),Phillips, Vieira, Hernandez, Roofe (Lasogga 78), Ekuban (Samuel 46). Unused substitutes: Lonergan, Anita, O’Kane, Struijk.
Referee: Tony Harrington (Cleveland).