Jurgen Klopp's side controlled most of the match and deserved to take the lead when James Milner converted from the penalty spot - but Spurs eventually burst into life with half an hour remaining.
A succession of thwarted chances preceded a beautifully-taken goal from Rose, although it was some woeful defending that presented him with the chance to secure a second draw in three Premier League matches this season.
A lively encounter in north London was then up for grabs, with Spurs looking the more likely winners after staging a series of late attacks.
Liverpool striker Daniel Sturridge arrived from the bench in the closing stages having been dropped from the starting line-up days after expressing his frustration at playing in a wide role during the 2-0 defeat at Burnley.
Divock Origi was chosen as the early replacement for Philippe Coutinho with Sturridge confined to a limited supporting role.
Five minutes into the match and Liverpool should have taken the lead, but Michel Vorm produced a brilliant save after Coutinho pulled the trigger from point blank range.
The chance came against the run of play as Tottenham had made the brighter start, but visiting goalkeeper Simon Mignolet was soon forced into action when Christian Eriksen floated in a tricky free-kick.
Gradually Liverpool began to take control of the game with their rapid passing and speed of thought putting Spurs on the back foot.
Kyle Walker was replaced by Vincent Janssen in the 28th minute due to feeling unwell and it was possibly the full-back's illness that meant Coutinho was left unmarked at the far post, with Vorm again coming to the rescue.
Both managers were animated as they strode around their technical areas, Klopp shouting out in protest when Jan Vertonghen escaped a penalty for tugging Joel Matip's shirt - but the Liverpool boss could at least be happier with his team's display.
Tottenham were being overrun and they finally cracked in the 43rd minute when referee Bobby Madley pointed to the spot.
Erik Lamela clipped Roberto Firmino as he darted into the area and although the contact did not appear to be deliberate, the penalty was given and Milner gave Vorm no chance.
Liverpool appeared to have doubled their lead after Spurs had been caught on the counter, but once Sadio Mane had tucked the ball home the flag went up for offside against Adam Lallana.
It was a marginal call that bewildered Klopp, but of greater concern to manager Mauricio Pochettino was the way in which his side gave the ball away and were then sliced open by Georginio Wijnaldum, Lallana and Mane.
Shortly after the hour mark, Spurs finally burst into life with Mignolet getting fingertips to a free-kick by Lamela before parrying clear a powerful header from Toby Alderweireld.
The balance had shifted and in the 72nd minute the home side levelled through Rose.
Eric Dier was able to escape down the right and when Liverpool flapped over his cross, Rose pounced from an acute angle at the far post by driving home a terrific finish.
Pochettino celebrated wildly, jumping in the air and pumping his arms before a group of Spurs fans, but his heart was in his mouth when Vorm got behind an injury-time effort from Wijnaldum.
Source : PA
Source: PA