Tottenham held on for a 1-1 draw against Real Madrid on Tuesday to draw level on seven points with the Champions League holders at the top of Group H.
Cristiano Ronaldo nearly had the hosts ahead at the five-minute mark, but his header from close range from a Achraf Hakimi pass hit the post before Karim Benzema side-footed the rebound wide.
And Ronaldo had another chance at the opener go begging before 20 minutes, with his right-footed shot from just inside the penalty area skirting wide of the post.
A lively looking Spurs side found their goal in the 27th minute when Raphael Varane inadvertently poked a Serge Aurier cross into his own net while under pressure from Kane.
Real were squarely on the front foot as they chased the equaliser, and it came before the break when Ronaldo converted a penalty after Aurier tripped Toni Kroos in the area and the referee pointed right to the spot.s
Hugo Lloris kept out a sure second for Real early in the second half, somehow getting a foot on a Benzema header from close range to preserve the 1-1 scoreline.
The France international goalkeeper was called into action again soon after, keeping out a deflected Isco shot before diving low and to his left to stop a well-struck shot from Ronaldo.
Fernando Llorente then teed up Kane perfectly in the 71st minute only for the in-form Spurs striker to see his shot from 10 yards palmed wide of the post when a goal seemed certain.
The other Group H match saw the shock result of the day as Borussia Dortmundremained without a win after a 1-1 draw by Apoel Nicosia.
The visitors struggled to break down their Cypriot opponents and found few chances in the opening 45 minutes, with Apoel's keeper Boy Waterman being substituted before half-time following a hard collision with Pierre-Emerick Aubameyang.
A horrible gaffe from Roman Burki gifted Apoel their goal. The Dortmund keeper's pass from his goal line was intercepted by Mickael Pote, whose first shot was saved by Burki only for the rebound to fall back to the Apoel man to fire home and make it 1-0.
Under pressure, Dortmund responded quickly, when Sokratis Papastathopoulos was able to head a looped Mario Gotze ball inside the far post.
Dortmund had a golden chance to find a winner on the last play of the game as Christian Pulisic played a fine cross to Aubameyang, whose header was saved up against the post, and Marc Bartra's follow-up somehow went over the bar.
Liverpool scored three times in the opening 20 minutes and went on to rout Maribor 7-0 for their first win in Group E.
The Premier League side needed a little more than three minutes to take the lead as Mohamed Salah jumped on to a loose pass and carried the ball into the box before crossing for Roberto Firmino, who dragged his back foot to turn the ball in.
And nine minutes later Philippe Coutinho doubled the lead by volleying James Milner's cross inside the near post.
Maribor's calamitous defending continued and Salah got on the scoresheet himself in the 20th minute after Roberto Firmino played him in on goal with a through ball.
Salah then added his second goal five minutes before the break by turning in Alberto Moreno's cross from close range, just beating Firmino to the ball.
But Firmino did get his brace early in the second half by flicking on a header after a Coutinho free kick, and Alex Oxlade-Chamberlain came on to score a late sixth before Trent Alexander-Arnold made it seven in stoppage time.
Despite only managing draws in the opening two games, Liverpool top Group E on goal difference above Spartak Moscow, who earned a 5-1 win at home over Sevilla.
The Russian champions found the opening goal in the 19th minute as a pass into the middle deflected out to Andrei Eshchenko, whose cross was met by the head of Quincy Promes.
Sevilla equalised following a corner on the half-hour mark, Simon Kjaer scoring with a left-footed volley after his original header was blocked.
But Lorenzo Melgarejo put Spartak back in front by curling in a first-timed shot in the 58th minute, and Denis Glushakov added a third goal from a volley nine minutes later.
Luiz Adriano netted the fourth on a 74th-minute counter-attack before Promes completed his brace in the final minute.
Manchester City made it three wins out of three in Group F by defeating Napoli 2-1.
Raheem Sterling put City ahead after nine minutes. David Silva cut a ball back from the byline, and though his pass went through the legs of of Gabriel Jesus it came to Kyle Walker -- whose shot was blocked -- before it fell to Sterling to score.
Gabriel added a second just four minutes later by tapping in a perfectly placed low cross from Kevin De Bruyne, who nearly scored himself in the 25th minute only to be denied by the underside of the bar.
Napoli had a chance to get back in the game before half-time when Walker hauled down Raul Albiol while defending a corner, but City goalkeeper Ederson Moraes denied Dries Mertens from the penalty spot
Moraes could not stop a second penalty as Amadou Diawara netted in the 73rd minute after Fernandinho brought down Faouzi Ghoulam, but City remained in control to see out the win.
City maintained their three-point lead over Shakhtar Donetsk, who rallied to earn a 2-1 win away to Feyenoord, who are still looking for their first point.
Steven Berghuis gave the hosts an eighth-minute lead by putting in a rebound with a diving header after Andriy Pyatov could only parry Tonny Vilhena's swerving shot from distance.
But Shakhtar hit back and levelled the score in the 24th minute from Bernard, who ran onto a through ball from Fred before rounding the keeper.
Bernard then put Shakhtar ahead nine minutes after the break by heading in Bohdan Butko's cross, and though Yaroslav Rakitskiy was sent off in the 75th minute, the Dutch side could not find an equaliser.
In Group G, Besiktas continued their perfect start to the campaign, beating Monaco 2-1 with a Cenk Tosun double to reach nine points at the top of the table.
Radamel Falcao got the scoring going for Monaco right on the half-hour mark, turning his right-footed shot home from a Keita Balde assist to make it 1-0.
However, the lead would last less than five minutes, as Tosun poked home a Ricardo Quaresma cross from very close range to put things back on level terms.
And the visitors were in front soon after the restart, with Tosun slotting home his second of the match from a Ryan Babel assist to secure the three points.
RB Leipzig earned an important three points against Porto, riding three first-half goals to a 3-2 win to leapfrog their Portuguese rivals into second place on four points in Group G.
Leipzig were ahead in the eighth minute when Willi Orban scored at the back post following a corner kick to give the hosts an early 1-0 lead.
But 10 minutes later, Porto were back on level terms when Vincent Aboubakar's left footed shot from a headed Felipe pass found the back on the net.
The scoring didn't let up in a five-goal first half, with Emil Forsberg and Jean-Kevin Augustin extending Leipzig's lead before Ivan Marcano pulled one back for Porto.