Andre Villas-Boas's side climbed to fifth in the table after second half goals from Steven Caulker and Aaron Lennon gave Tottenham their fourth successive Premier League win.
Tottenham played some of their best football of the season and such was their dominance over Villa that French goalkeeper Hugh Lloris, finally making his league debut, had little to do.
It was another chastening experience for former Norwich boss Lambert, who has managed just one win from his first seven league matches since taking charge in pre-season, and Villa have dropped to a lowly 16th place.
Villas-Boas sprang a surprise before kick-off when he ended American goalkeeper Brad Friedel's run of 310 consecutive Premier League starts by giving Lloris his top-flight debut.
Lloris, signed from Lyon for £8 million on deadline day, helped Spurs to their first Premier League cleansheet of the season.
But most of the action was at the other end of the pitch and, with less than 30 seconds gone Jermain Defoe laid the ball off to Gareth Bale, who flashed a curling shot just wide.
Jan Vertonghen then burst down the left flank and cut the ball back but Defoe blazed the ball over from 12 yards.
Lloris' first piece of action came after 20 minutes when he saved from Christian Benteke, but Spurs were soon back on the attack and Defoe shot just wide.
Villa intercepted a sloppy Lloris throw to Vertonghen and Gabriel Agbonlahor found the unmarked Benteke at the back post but he headed wide.
That proved Villa's last serious chance to win the match as Spurs took the lead in the 58th minute.
Defoe got on the end of Bale's cross and took a touch before firing a low shot that was going wide until it clipped Caulker's heel and flew past Brad Guzan.
It was 2-0 nine minutes later as Lennon scored his first goal of the season.
Villa defender Joe Bennett failed to close down Clint Dempsey, who squared for Lennon and he swept a precise shot past Guzan in to the far corner.
Dempsey should have put the game beyond doubt 15 minutes from the end, but he somehow missed a free header from eight yards.
To make matters worse for Villa, Bennett was carried off on a stretcher with 12 minutes left after clattering in to the advertising boards.
Tottenham Hotspur sink Aston Villa 2-0
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