Dier provided the perfect finish to a fine move in the 93rd minute - our 50th Premier League goal against the Hammers - to secure three points in Mauricio Pochettino's first match as Head Coach.
Earlier, Dier formed part of a dogged defensive display after we were reduced to 10 men following Kyle Naughton's red card for handball in the 30th minute.
However, Mark Noble missed the spot-kick and we repelled everything the Hammers had to throw at us until the numbers were levelled up on 64 minutes when James Collins picked up his second yellow card to follow Naughton down the tunnel for an early bath.
It looked like ending 0-0 - until Dier capped an impressive display with the winner to send the Spurs fans into raptures.
Mauricio named his first Spurs team for a competitive fixture without the players who featured in the latter stages of the World Cup - Paulinho and the Belgian contingent - while handing a debut to Dier alongside captain Younes Kaboul - his 100th Premier League appearance for us - at the back.
Nabil Bentaleb and Etienne Capoue held the midfield enforcer roles, with playmakers Erik Lamela, Aaron Lennon and Christian Eriksen ahead of them and behind target man Emmanuel Adebayor.
A keeper - West Ham's Adrian on this occasion - was called into action for the first time on eight minutes when he routinely fielded an Eriksen free-kick. The game certainly did not explode into action from the off, more gentle sparring and probing, as opposed to any kind of onslaught.
Territory-wise, it was the men in white shirts looking the most assured and slightly more on the front foot, but without causing too much anxiety among the home crowd.
West Ham began to exert a little bit of pressure towards the midway point of the half, with a more direct style causing some uncertainty at the back, but nothing that resulted in Hugo Lloris having to become involved in play.
Kevin Nolan nodded wide from a Joey O'Brien cross before Carlton Cole squared across the area, forcing Danny Rose into an emergency clearing operation at the back post. Those in claret and blue were lifted and the atmosphere momentarily increased in volume.
It cranked up further when, in the 28th minute, a corner was allowed to be nodded back into the danger zone and Nolan tried a shot on the turn that was blocked by the close attendance of Naughton. Probably unavoidably, Naughton's arms played a part in the block and after prompting from his assistant, referee Mr Foy pointed to the spot and also showed red to Naughton.
Noble then shot wide with his penalty, but the penalty of playing with 10 men remained.
Capoue slotted in at the back alongside Kaboul, with Dier moving right to cover for the absence of Naughton. Ricardo Vaz Te flashed across goal on 37 minutes as West Ham sought to capitalise on their numerical advantage.
A darting run by Lamela and lay-off from Adebayor presented Lennon with a shooting chance shortly before the break that dipped just over the bar.
Lloris was tested for the first time eight minutes into the second half by a stinging low drive from Cheikou Kouyate, but West Ham were struggling to make inroads against the 10 men.
Eriksen was looking most likely to unlock the gate at the other end but, for the most part, this was turned into a rearguard action with the Dane and Lennon dropping deep to protect the back four.
Lewis Holtby and Andros Townsend made their entrance with 30 minutes left on the clock, taking over from Lamela and Lennon.
The numbers were then level due to Collins seeing yellow for the second time, hauling down Adebayor.
Townsend fizzed in an effort that Adrian needed two hands to divert over, before the winger tried again with a shot that was diverted across goal. The arrival of the England winger and Holtby did introduce a new energy to a side that had been on the back foot since the sending off of Naughton.
A mix up between Bentaleb and Kaboul allowed Noble to home in on goal and only a smart save from Lloris prevented the deadlock being broken in a careless fashion.
Harry Kane was next to join play with nine minutes of normal time remaining, taking the place of Adebayor.
Lloris then made what turned out to be a match-winning, point-blank save from Downing with only three minutes remaining.
Adrian did well to turn away Bentaleb's stinger as we ticked into four minutes added time - and then the moment that really mattered.
Kaboul pinged a pass into Kane, he picked out Dier's run across the back line from right to left and through on goal, the England Under-21 international provided a nerveless finish, skipping past Adrian and slotting home.
West Ham: Adrian; O'Brien (Demel, 62), Collins, Reid, Cresswell; Downing, Kouyate, Noble, Nolan, Vaz Te (Diame, 68); Cole (Valencia, 81). Subs (not used): Jaaskelainen, Zarata, Poyet, Burke.
Spurs: Lloris; Naughton, Dier, Kaboul (C), Rose; Bentaleb, Capoue; Lennon (Townsend, 61), Eriksen, Lamela (Holtby, 61); Adebayor (Kane, 83). Subs (not used): Friedel, Davies, Dawson, Soldado.
Goals: Spurs - Dier (90+3).
Yellow cards: West Ham - Collins, Kouyate.
Red cards: West Ham - Collins (second yellow). Spurs - Naughton.
Referee: Mr C Foy.