Kane's departure was confirmed on Saturday, with the England captain ending his time at the club in order to search for trophies at German champions Bayern Munich.
Cristian Romero sent Ange Postecoglou's side into an 11th-minute lead on Sunday, but Brentford turned the match around through goals from Bryan Mbeumo and Yoane Wissa.
Tottenham managed to level in the latter stages of the first period through Emerson Royal, though, and there were no further goals in the second 45, with the points ultimately being shared.
Kickoff was slightly delayed at the Gtech Community Stadium due to the fact that no water was coming into the stadium, but the contest did eventually get underway at 2.07pm local time.
Tottenham made the breakthrough in the 11th minute of the contest, with Romero heading a brilliant James Maddison delivery into the back of the net from close range.
There was a check for a possible offside, and it was incredibly close, with the Spurs players and fans facing an anxious wait, but Romero was just about played on by the final Brentford defender.
Romero was replaced shortly after with a potential concussion, and Brentford then created their first real opening in the 16th minute, with Mbeumo's effort stinging the palms of Spurs debutant Guglielmo Vicario.
Wissa was then denied by Vicario in the 18th minute, before a mistake from Davinson Sanchez almost allowed Mathias Jensen in, with the home side taking the match to Tottenham in a bid to level the scores following the early setback.
Brentford had a shout for a penalty in the 23rd minute when Son Heung-min brought Jensen to the ground inside the box; the play initially continued, but the referee was then sent across to the monitor following advice from VAR before awarding the penalty to the hosts.
Mbeumo stepped forward in the absence of Ivan Toney and expertly found the back of the net with a cool finish, sending Vicario the wrong way in the process.
Brentford then turned the match around in the 36th minute, with Wissa's deflected effort finding a route into the back of the net after Micky van de Ven had stuck out a leg in front of his goalkeeper.
Spurs had more of the ball in the closing stages of the first period, and the visitors managed to level the scores in the fourth minute of added time when Emerson found the back of the net with a low strike from just outside the box.
Mbeumo should have sent Brentford back ahead deep into the 11 minutes of additional time at the end of the opening 45 minutes, but the forward somehow fired a cross from Rico Henry wide from close range, with the two teams level at the end of a brilliant half of action.
Maddison tested the gloves of Brentford goalkeeper Mark Flekken early in the second half, with Spurs making the faster start to proceedings after the break.
Brentford twice came close to regaining the lead just before the hour, but Vicario was on hand to keep out a strike from Henry before the Spurs debutant then denied substitute Mikkel Damsgaard.
Flekken then did well to keep out a strike from Son, before the Brentford goalkeeper made an even better stop to deny Richarlison in the 64th minute during an open period of the match.
The Bees had another penalty shout in the 78th minute when Van de Ven appeared to foul Kevin Schade inside the box, but following a VAR review, it was decided that the centre-back had won the ball.
Schade lifted one over the crossbar shortly after Mathias Jorgensen had looped a dangerous cross towards the far post, which caused Vicario plenty of problems.
Tottenham put the pressure on in the latter stages, but there was to be no late drama in West London, with the points ultimately being shared at the end of an entertaining clash.
Spurs will continue their league season at home to Manchester United next Saturday, while Brentford face a trip to Fulham on the same afternoon.