Jurgen Klopp's side moved two points clear of Manchester City once more at the top of the table, but City have a game in hand.
Liverpool's hopes of ending a 29-year wait to win the title looked set to be dealt a massive blow as Lucas Moura's strike 20 minutes from time cancelled out Roberto Firmino's early opener.
However, Hugo Lloris could only palm Mohamed Salah's header into the path of the unfortunate Alderweireld to condemn Tottenham to a fourth defeat in five Premier League games.
Spurs are now in serious danger of crashing out of the top four as they remain level on points with Manchester United and there's also Arsenal in the run.