The England international fired home to cancel out James Milner's first-half penalty and make it three draws in the last three meetings between the sides.
Jurgen Klopp had criticised his team's decision-making in last Saturday's shock 2-0 loss at Burnley and Philippe Coutinho twice spurned excellent chances to open the scoring in the first half, with Michel Vorm saving well.
Spurs struggled to threaten Simon Mignolet's goal for much of the first hour and Liverpool looked likely to double their lead, with Joel Matip hitting the crossbar and Sadio Mane's tap-in ruled out for offside.
But the visitors began to sit deeper as fatigue set in and Rose took advantage of some slack defending to drill home an equaliser preserve Spurs' unbeaten start to the campaign.
Mauricio Pochettino's side started well, but had Vorm to thank for a brilliant save to deny Coutinho with just four minutes played, the former Swansea City man sticking out a foot to deny the Brazilian who was unmarked just six yards from goal.
Christian Eriksen saw a free-kick beaten away by Mignolet and Dele Alli sliced a promising opening wide from 18 yards out as Spurs continued to look the more dangerous early on.
Liverpool, having begun to settle, applied some pressure of their own and it took two superbly timed sprints from goal from Vorm to deny Sadio Mane and Georginio Wijnaldum, before he saved another low shot from Coutinho from close range.
