The Slovakian striker pounced to slot home the winner with 16 minutes left of a pulsating second half.
Massimo Maccarone stepped over a pass from the left touchline and Nemeth was onto it in a flash, evading Dean Richards' last-ditch tackle, skipping around Kasey Keller and rolling the ball home.
The result capped a miserable few months against the Teesiders, who beat us 5-1 at the Riverside last May and knocked us out of the Carling Cup on penalties at the Lane in December having picked up a Premiership draw in October. Few Spurs fans will book their holidays flying out from Teeside Airport, that's for sure.
Nemeth's goal came as we looked to have ridden the storm in the second half.
Boro got on top after we'd played all the football in the first half and Keller was at his best to keep the home side out.
First he tipped over a Juninho drive destined for the top corner and then saved Maccarone's spot kick after Richards was harshly penalised for what looked like a ball-winning tackle on Job.
But it wasn't to be and despite a couple of late efforts - Robbie Keane's shot whistled inches wide - and ending with Keane, Jermain Defoe, Helder Postiga, Gus Poyet and Stephane Dalmat all on the pitch, Boro's twin towers of Gareth Southgate and Ugo Ehiogu held firm.
An even first half of few chances was illuminated by two spectacular efforts from Defoe and Darren Anderton.
Defoe's flick up and volley from 18 yards flew a yard over as our passing game dictated the opening spell.
Keller had to be alert to flick Boudewijn Zenden's inswinging free-kick over before the highlight of the half, Jackson floated the ball out to Anderton from a corner and the midfielder cracked a first-time volley towards goal from 20 yards - Mark Schwarzer was ready for it and tipped over.
The arrival of Maccarone off the bench at half-time sounded alarm bells with his recent record against Spurs but he fluffed his lines on the hour.
Juninho's pass was perfect for Job to latch onto in the box but Richards appeared to avert the danger with a sliding tackle - not according to referee Mark Halsey, who pointed to the spot.
Maccarone took the responsibility but Keller guessed right - to his right - and managed to palm the effort around the post.
Job then somehow missed from six yards after Richards miskicked and we started to fight our way back into it, Ledley King the pick in midfield.
There was little Keller could have done about the goal, although maybe it might have been cut out at source. A ball from the left side released Nemeth, who held off Richards, beat Keller and slotted home.
Keane was inches away from a leveller when his 20-yarder flashed just wide, Helder Postiga might have done better from the edge of the area and Keane looked impeded by Ehiogu - more of a penalty than the one awarded - but it wasn't to be again in the north-east.
MINUTE BY MINUTE GUIDE
8mins: Defoe flick up and spectacular volley from edge of the area flew a yard over.
10mins: Keane tricks and appeared to be blocked by Ehiogu in box, no appeals though.
23mins: SAVE. After we'd dictated possession for first 20 minutes, Keller forced into first save, quick feet to reach and tip over inswinging Zenden free-kick.
24mins: Job worked an opening after battling it out with Carr and Anderton, tame shot hacked away by Gardner.
30mins: Brilliant sliding interception from Ehiogu as Brown attempted to release Defoe.
36mins: SAVE. Corner routine saw Jackson pick out Anderton 20 yards out, full volley heading for top corner before Schwarzer's full-length intervention.
Injury time: YELLOW. Brown for foul on Zenden.
Half-time: Middlesbrough 0-0 Spurs
Half-time: SUBS. Parnaby and Maccarone for Doriva and Davies.
47mins: SAVE. Juninho found a yard in the box and rifled towards top corner, Keller's fingertips diverted it over.
49mins: Anderton blasted over from 25 yards.
55mins: Brown skipped away from Zenden, low drive well fielded by Schwarzer.
56mins: Taricco low shot from 22 yards bounced in front of Schwarzer but gathered with little fuss.
60mins: PENALTY/SAVE. Looked like a poor decision as Richards appeared to win ball as Job broke through. Not the best of spot kicks from Maccarone, Keller guessed right to his right and palmed around post.
64mins: MISS. Amazing miss, ball bobbled over Richards' attempted clearance, Job clear in front of goal, six yards out, somehow side footed wide.
65mins: SUB. Dalmat for Jackson.
68mins: SUB. Nemeth for Job.
74mins: GOAL. Maccarone stepped over ball from left touchline, Nemeth got to it ahead of Richards, cleared tackle, nipped around Keller and slotted home. 0-1.
80mins: CLOSE. Superb pass from Anderton to turn defence into attack, Defoe and Carr involved before Keane unleashed shot inches wide from 25 yards.
82mins: SUB. Poyet for Brown.
85mins: YELLOW. Carr for foul on Juninho.
87mins: SUB. Postiga for Anderton.
88mins: CHANCE. Carr pass released Postiga, decent shooting chance from 20 yards but scuffed it wide.
Injury time: PENALTY? Keane onto Mendieta mistake, got around Parnaby, appeared to be held back by Ehiogu.
Line-ups: Middlesbrough: Schwarzer, Queudrue, Ehiogu, Southgate, Boateng, Juninho, Mendieta, Job (Nemeth, 68), Doriva (Maccarone, 45), Davies (Parnaby, 45), Zenden. Subs: Jones, Riggott.
Spurs: Keller, Carr, Taricco, Gardner, Richards, King, Brown (Poyet, 82), Anderton (Postiga, 87), Jackson (Dalmat, 65), Keane, Defoe. Subs: Burch, Doherty.
Referee: Mike Halsey.
Szilard Nemeth made sure it was more agony against Middlesbrough with a late winner at the Riverside on Tuesday night.