The Lilywhites were heading for an early exit from the competition after PSV held firm following Luuk de Jong's opener just 61 seconds into the contest.
Tottenham's pressure finally told in the final 12 minutes, however, as Harry Kane led from the front by netting a couple of goals to lift his side to within three points of Inter Milan, who earned a 1-1 draw against Barcelona elsewhere tonight.
Victory for Tottenham knocks 24-time Dutch champions PSV out of the Champions League, and sets up a huge shootout with Inter at Wembley in three weeks' time.
Spurs, winless in a club-record five Champions League matches prior to tonight, responded well and had a number of first-half chances to draw back on level terms.
Kane was also kept out by Jeroen Zoet a quarter of the way through the match - one of four saves the visiting keeper would make in a first half the home side would go on to dominate without scoring.
Zoet produced a double stop to keep out Christian Eriksen's first-time shot from six yards out and Alli's follow-up, which the Englishman - one of six players to be brought back into the starting lineup - should have been burying.
The direct Lucas Moura was proving a real threat, and he would also be denied by Zoet at the end of a mazy run, as was Alli for a second time later in the half.
Tottenham continued to dictate the flow of the game in the opening 20 minutes of the second period, but the closest either side came to a goal was through Pereiro's rising header, which Paulo Gazzaniga - in for the suspended Hugo Lloris - was equal to.
A deflected Son Heung-min shot ended in the side-netting and Ben Davies had a low shot saved as the home side, without back-to-back Wembley wins since the opening month of the season, were held at arm's length.
That all changed 12 minutes from time, however, as Kane exchanged passes with substitute Fernando Llorente and swept the ball past Zoet to give his side's European hopes a much-needed boost.
Donyell Malen and Llorente both came close in the final 10 minutes, the former shooting too close to Gazzaniga and the latter heading right at Zoet, setting up a thrilling conclusion as Kane proved the hero again.
The Tottenham skipper got his head to Davies's cross and saw it creep over the line via a couple of deflections off Trent Sainsbury and Daniel Schwaab, keeping Tottenham alive in Group B and eliminating PSV in the process on a dramatic night in the English capital.
TOTTENHAM HOTSPUR (4-3-3): Gazzaniga; Aurier (Trippier 75'), Alderweireld, Sanchez, Davies; Eriksen, Dele, Winks; Lucas (Lamela 62'), Son (Llorente 75'), Kane
PSV EINDHOVEN (4-3-3): Zoet; Dumfries, Schwaab, Viergever, Angelino; Rosario, Hendrix, Pereiro (Malen 73'); Bergwijn (Gutierrez 86'), De Jong (Sainsbury 81'), Lozano