Son Heung-Min scored the opening goal for Spurs in first half stoppage time, but it was Alli's 58th minute that gave Spurs some much-needed breathing room.
The goal was Alli's 50th in all competitions for the club, Since the start of 2015-16, only Son and Harry Kane have more for Spurs in all competitions.
With the midfielder's finish, the trio have all now eclipsed the 50-goal mark with Son on 52 and Kane at 117.
No other Premier League club has seen more than two players do so since the 2015-16 campaign.
Son's finish gives him three goals in his last four league games after the South Korean star hadn’t netted in any of his previous 15 prior appearances for the club.
That 16-game total is their best ever start to a Premier League season.
Only twice before have they had a better total after 16 matches in a top-flight campaign with the 46-point total in 1960-61 and 37-point haul in 1956-57 setting the benchmark based on three points for a win.
Following that, the club returns to the Premier League against Burnley.