The home side thought they’d won it when Salah’s quick feet led to him getting free in the area and scoring in injury time, but a moment of madness from Virgil van Dijk, bringing down Érik Lamela in the 94th minute, offered Kane the chance of redemption.
He took his chance this time, sending Karius the wrong way with the last kick of the game to ensure Spurs took a point back to London and kept within two points of third-placed Liverpool.
Here are five things we learned from the match.
Van Dijk goes from hero to zero
It’s been an up-and-down start to his Anfield career and that was summed up today.
After his debut against Everton, the £75million they paid was hailed as a bargain.
Yet, just a couple of weeks later, he was overpriced after his mistake failing to properly clear the ball against Swansea City saw Liverpool lose their 18-match unbeaten run.
For 93 minutes, it was the perfect performance from the former Southampton man.
His comfortable nature on the ball here was clear, striding out from the back, with his passing ability making him look more like a midfielder than a centre-back at times.
Defensively, he was solid too, with a block from Son Heung-Min in particular during the first half showing why exactly they’d paid the money for the Dutchman.
He also was a threat in attack, especially from set pieces.
It felt like he was the leader of the team, yet his foul on Lamela with just seconds left meant his side went away without the three points they should really get when they score an injury-time goal.
He went from the rock of the Reds’ defence to the villain with one rash moment. Liverpool fans will hope he doesn’t fall victim to the catastrophic individual mistakes that so often sums up the Reds’ back line under Jürgen Klopp.
Trent Alexander-Arnold will be a future England star
At just 19, Trent Alexander-Arnold produced a really assured performance.
He isn’t only solid in defence, but going forward he offers Liverpool a great outlet.
The English youngster has a great level of passing and crossing ability, knowing when to pick his man out and when to drill the ball into the box. He caused Ben Davies all sorts of problems when he was bombing forward, particularly in the first half.
It would be a real surprise if he doesn’t become an England right-back in the next few years. More performances like this from now until the end of the season could even see him be in the squad for Russia.
The right-back was booked for a heavy challenge on Davies. There were some calls for it to be a red, but it was fair for him to see yellow.
Spurs need to address their poor away record
Tottenham have been up there with the very best sides over the last two-and-a-half seasons in the Premier League, yet they’ve got nothing whatsoever to show for it.
Today underlined why.
They went into the tie with just one win away to fellow top six teams in their last 20 attempts.
Their Anfield record was pretty disappointing too, with just one win in their last 23 visits.
Salah’s early goal meant it was now 29 games in a row away at big-six sides where they’d failed to keep a clean sheet.
If they want to truly have a chance of winning the Premier League, they need to sort this record out. You need to beat the best to be the best to speak in football clichés.
Tottenham were the better side for much of the game, but still they couldn’t win.
If Kane had scored his first penalty, they surely would have done.
They may have fought back twice to get a draw after falling behind but they need to taste victory away from home at the big sides if they want to be Premier League champions some time soon.
Liverpool: Premier League counter-attack kings
Tottenham showed just how dangerous it is to push up and leave gaps behind your defence against Liverpool.
With just two minutes on the clock, Firmino found himself with the ball in the Spurs half. Eric Dier’s panic at dealing with the Brazilian led to a poor backpass which found Salah.
Due to Spurs’ relatively high line, he used his pace to go through on goal, sending Hugo Lloris the wrong way and giving the Reds an early lead.
They never stopped pressing, and pounced on mistakes at the back – after 11 minutes, Sadio Mané forced Davinson Sánchez into making a mistake, with Spurs only surviving due to a last-ditch Dier block.
Spurs undoubtedly came back into the game the stronger side later on, but they were always chasing the match, and with Liverpool’s pace on the counter, having to push forward meant the Reds were always a threat.
Battle of the Premier League’s best forwards
Going into the game, Kane and Salah were the Premier League’s top two scorers and they were seen as the men who could make a difference for their side.
Kane had 21 goals (one assist) while Salah had 19 goals (six assists) before the game at Anfield got underway.
Yet, with two minutes gone, as we’ve already mentioned, the Egyptian showed why he’s been arguably the signing of the season since his move from Roma.
His early opener made him the quickest player to get to 20 Premier League goals in Liverpool history, managing the feat in just 25 games.
Salah wasn’t completely faultless of course, on occasion using his pace to break quickly, but making the wrong decision. If he’d managed a slightly better pass, he could have extended the home side’s lead, killing off Tottenham before they had the chance to get into it. But by scoring Liverpool’s two goals, he underlined his role as their talisman up front.
Kane, by contrast, started the game very slowly, not touching the ball until the 12th minute.
Even when Spurs were pushing forward, the Spurs No.10 was never really particularly close to scoring until the last five minutes.
He had the perfect chance to kill off the match, after being fouled by Karius in the box, stepping up to take the resulting penalty. His awful effort was straight at the Liverpool keeper though, as he still searches for his 100th Premier League goal.
He more than made up for it though, by smashing in a 94th-minute penalty.
That was his 100th Premier League goal, in just his 141st appearance in the competition. Pretty impressive indeed.