Villa won at Spurs' stadium, increasing the pressure on the manager.
In his first game back after the World Cup, Hugo Lloris made a mistake that allowed the other team to score.
After falling out of the top four on Saturday, Spurs have only won two of their last seven games.
Villa have won their last two away league games.
The contest was supposed to pit the two keepers who faced off in the World Cup final penalty shootout against each other, but Argentina's spot-kick hero didn't make it.
The match was not good for the returning finalist. The World Cup-winning defender was shown a yellow card in the first half for barging Philippe Coutinho, while the captain of the team, Hugo Lloris, was shown a red card in the 50th minute.
Buendia was able to score after he spilled Luiz's long-range effort.
Luiz started and finished the move for 2-0, sliding a pass to John McGinn before racing on to receive the return and chip past Lloris.
Some fans directed angry chants towards chairman Daniel Levy at the end of the game.
After losing their place in the top four to Manchester United, the onus was on Spurs to perform better.
While they did improve on their previous five games by not trailing at half-time, Spurs continue to look disorganized, exemplified after 18 minutes when Son Heung-min ripped off the protective mask he wore during the World Cup.
Kane came deep into the middle of the field to get the ball after barely touching it in the beginning.
The England captain had a chance to open the scoring.
Kane was played in over the top before being forced wide by the keeper, but he was able to get a cross back over for him. After initially playing onside, Young directed the effort behind for a corner.
After Buendia's opener, the ball fell 15 yards out and he missed the goal.
In seven consecutive games, Spurs conceded at least two goals.
Bryan Gil made his first league start in place of the injured Dejan Kulusevski, but was replaced just past the hour after an anonymous display, and as his side slipped towards another worrying defeat.
Emery was able to get the better of Spurs in three of the four games they played against him.
He defended his decision to leave a World Cup winner on the bench.
Emery named an unchanged team from the one that lost to the Reds on December 26th.
He was given something. Watkins and Buendia were bright to pounce on the opening that Lloris gave them.
They made it possible for Emery to win his first two away matches.
Ossie Ardiles was the previous record holder for the most games in charge without being involved in a goalless draw.