Liverpool beat Arsenal 4-3 at Emirates Stadium on the opening weekend of the Premier League season and were in control through James Milner's penalty, scored just before the break after Erik Lamela fouled Philippe Coutinho.
Tottenham goalkeeper Michel Vorm had earlier saved brilliantly from Coutinho, and Joel Matip had glanced a header off the bar, as Liverpool tried to make the most of their superiority.
Mauricio Pochettino's side finally roused themselves and after Liverpool keeper Simon Mignolet saved superbly from Toby Alderweireld's header, Rose arrived at the far post to take Eric Dier's cross under control and drive in a low finish to earn Spurs a point.