Villa had started Friday in sixth, one of six teams battling for the four remaining Champions League places along with league winners Liverpool.
The victory lifted Unai Emery's men to 66 points, two points behind second-placed Arsenal, equal with Newcastle and one above Manchester City.Â
All three teams have a game in hand, as do Nottingham Forest, who are seventh with 62 points.
Chelsea, who were playing Manchester United later on Friday, started the night with 63 points, and were also in the running in the tight battle for a place in Europe's top competition.
Spurs boss Ange Postecoglou rested several regular starters ahead of next week's Europa Conference League final against Manchester United, with both the matches brought forward by 48 hours to allow the finalists to prepare for the Bilbao clash.
On a tense night at Villa Park, the home side had the better of the play but were forced to wait until the 59th minute to get the opener.
Ollie Watkins steered John McGinn's corner back across goal and an unmarked Ezri Konsa turned the ball into the net.
Boubacar Kamara then doubled the lead with a low drive from the edge of the penalty area.
The result extended Villa's unbeaten home run to 21 games in all competitions, their best sequence since 1977, and left Spurs in 17th place in the 20-team league, now having suffered 21 top-flight league defeats this term.
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