Manchester City’s 4-0 victory at Newcastle earlier meant Liverpool could not top the league at Christmas for the first time in four years, with Jurgen Klopp’s side now three points adrift.
Harry Kane ended his Premier League goal drought when he found the bottom corner from Tanguy Ndombele’s pass but Spurs wasted a number of opportunities to double their lead.
Diogo Jota made the hosts pay on 35 minutes by heading in a cross from Robertson, who had missed a golden chance of his own in the opening 70 seconds.
Robertson then headed the Reds in front in the second half only for Son Heung-min to level after a mistake by Alisson four minutes later in an open and frenetic game.
Liverpool left-back Robertson had been excellent but was sent off for a reckless hack on Emerson Royal, a decision given after Paul Tierney reviewed the decision on the pitch-side monitor.
The draw extends Antonio Conte’s unbeaten league start at Tottenham to five games, though his side stay seventh with games in hand on those above them.
High drama after troubled week
On a weekend of depleted Premier League action, these sides served up a thrilling encounter packed with drama at the Tottenham Hotspur Stadium.
Both faced Covid-related interruptions to their own preparations and Klopp said beforehand the managers had no idea which players would be available until the morning of the game.
Tottenham had to close their first-team training facility for three days last week and have had three games in five days postponed, despite travelling to Leicester on Thursday, something Conte said had affected his squad’s morale.
Nine Spurs tested positive during the past fortnight, as well as staff and under-23s, meaning Conte was unable to implement his usual meticulous tactical plans and had to resort to mannequins as opposition, but it was Liverpool’s defence looking static as the hosts opened them up in north London.
Ndombele, making his first league start under Conte, showed his undoubted quality with a superbly weighted pass for Kane that the England captain swept into the far corner for only his second goal in the Premier League this season and first in seven games.
Conte has called Kane “one of the best I’ve had the pleasure to train” and the 28-year-old almost set up a second moments later, though Son could not turn his cross into the net.
The South Korean overran another Kane pass to allow Alisson to smother before Kane then dived in on Robertson and was perhaps fortunate to only receive a yellow card – a decision brought further into focus by Robertson’s own sending-off.
For all Liverpool’s pressure, Tottenham could have been out of sight with Dele Alli – another awarded a chance by Conte – the next to fail to convert a glorious chance from Son’s clever pass, although Alisson got a vital fingertip to his effort.
Liverpool were also missing a number of key players, with Virgil van Dijk, Fabinho and Thiago among those absent following positive Covid tests, while Jordan Henderson had a cold, allowing a first Premier League start for 19-year-old Tyler Morton, who was 10 days old when midfielder partner James Milner made his league debut in 2002.
Klopp could still call on his flying full-backs though and Robertson, after nodding wide from Trent Alexander-Arnold’s smart ball in the second minute, picked out Jota who steered an excellent header beyond Hugo Lloris for his 10th Premier League goal of the season.
The Reds boss was furious Jota was not awarded a penalty following a clumsy challenge by Royal but the German will also have been frustrated by his side’s continuing failure to deal with the Spurs threat after the break.
The visitors only survived going behind when Alli sold Kane short for a tap-in, allowing Alisson to make a decisive save, before Kane headed over from close range.
In a sequence that summed up the game, Spurs thought they should have had a penalty at one end only for Robertson to head in Alexander-Arnold’s cross from close range at the other.
Son then pounced on Alisson’s error to roll into an empty net before Scotland international Robertson’s kick on Royal was upgraded to a red card following referee Tierney’s review.
Amid the madness, Tottenham did stop Mohamed Salah scoring or assisting for what would have been a record 16th successive game.
And while second-placed Liverpool may have slipped further behind leaders City, the Reds’ impressive form continues and they have now lost just once in the past 35 games in all competitions.
Klopp’s side also scored their 50th Premier League goal of the season in what is their 18th match, reaching that landmark faster than in any other previous top-flight campaign.