Goals from Lucas Moura and Harry Kane had given Spurs the lead after Hirving Lozano broke the deadlock just before the half-hour mark, but a late sending-off for Hugo Lloris changed the course of the game.
Luuk de Jong soon equalised for the home side and although Spurs were able to hold on for a share of the spoils, Mauricio Pochettino's team effectively have to win each of their remaining three matches in Group B to maintain their hopes of reaching the knockout stages, a scenario which also applies to PSV.
Both teams started brightly at the Philips Stadion, but it took until just before the 15-minute mark for a clear chance to be created with Kane seeing a shot from 15 yards fumbled clear by Jeroen Zoet.
Kane then had an effort on the turn deflected over the crossbar, before the frontman powered a header against the angle after meeting an outswinging corner.
PSV hit back with Gaston Pereiro curling a free kick marginally wide of the near post, and De Jong should have done better from 12 yards instead of sending a header harmlessly over the crossbar.
Son Heung-min saw a low shot comfortably saved by Zoet back at the other end, but PSV went ahead in the 29th minute when Lozano dispossessed Toby Alderweireld close to the halfway line and saw his resulting effort from 12 yards deflect off the Belgian and loop over Lloris.
Spurs thought that they had found an equaliser soon afterwards when Davinson Sanchez fired into the bottom corner after a set piece was not cleared, but the officials deemed Kane to be in an offside position despite not having any impact on the play inside the six-yard box.
The visitors felt hard done by, but with six minutes of the first half remaining they were deservedly back on level terms when Moura fired a deflected effort into the roof of the net after collecting Kieran Trippier's cutback.
Spurs soon went onto the front foot after the restart as Christian Eriksen wasted a good chance from 20 yards, with the Dane's strike being well kept out by Zoet.
However, the North London outfit went ahead soon afterwards as Son and Eriksen combined on the left before the latter's cross was headed into the roof of the net by Kane from close range.
Spurs were beginning to dominate all aspects of the game and a third goal should have arrived when Kane was found at the back post by Trippier, only for Zoet to make a brilliant stop from the England skipper's header.
Substitute Erik Lamela was the next player to go close after collecting a pass from Kane, with the Argentine striking the crossbar from an acute angle, but Spurs gifted PSV a way back into the contest when Lloris was sent off for a professional foul on Lozano despite two defenders being well placed to deal with the danger.
Michel Vorm was instantly forced into action to keep out a free kick from De Jong, but the Dutch frontman got his team back on level terms with three minutes left when flicking the ball past the replacement stopper from 10 yards out after Spurs had failed to deal with a free kick from the left.
Both teams pushed for a winning goal, but the draw leaves the sides aware that the result of the reverse fixture at Wembley Stadium could potentially decide which club takes part in the Europa League after Christmas.
PSV EINDHOVEN (4-3-3): Zoet; Dumfries, Schwaab, Viergever, Angelino; Rosario, Hendrix, Pereiro (Gakpo 83'); Malen, De Jong, Lozano
TOTTENHAM HOTSPUR (4-2-3-1): Lloris; Trippier, Alderweireld, Sanchez, Davies; Dier, Dembele (Winks 74'); Moura (Lamela 64'), Eriksen, Son (Vorm 81'); Kane