Scholes broke the deadlock after 67 minutes before Van Nistelrooy's customary goal secured the points in injury time.
The final scoreline was a little harsh on the lads after a gutsy display, not least defensively - particularly the outstanding Ledley King - but there could be few complaints that the points went to the right home.
Unfortunately, Dean Richards limped off after 30 minutes with what appeared a calf injury to add to Glenn Hoddle's woes.
The first half was all about Van Nistelrooy against Keller and the American came out on top with four fine saves from the Dutchman.
Keller's reflexes were tested with just 20 seconds on the clock as Van Nistelrooy latched onto a ball over the top and lashed in a drive from 16 yards.
Roy Carroll was tested next as Matty Etherington burst onto Teddy Sheringham's pass and the winger's free-kick was flicked a yard wide by Dean Richards after 15 minutes.
United, so quick to break, created the next opening as Ryan Giggs, David Beckham and Scholes combined but Van Nistelrooy could only poke Giggs low cross wide from close range.
Gus Poyet's 25-yarder was fielded comfortably by Carroll before Keller's best save of the half, flinging out a hand to his left to take the pace off Van Nistelrooy's shot before Mauricio Taricco mopped up a yard out.
Then a blow as Richards was forced off, replaced by Anthony Gardner.
A minute later and it was Keller/Van Nistelrooy III, this time the striker's header from Beckham's cross tipped over.
Having had his reflexes tested, Keller next showed his bravery as Van Nistelrooy turned on a sixpence from Roy Keane's pass only to find the keeper at his feet to block.
It didn't take long for battle to recommence in the second half as Keller tipped over Ole Solskjaer's drive after 47 minutes.
A couple of blocks from the excellent King and Gardner the denied Solskjaer and Giggs and the Welshman fired just wide as United pushed on.
Van Nistelrooy then created something out of nothing, spinning away from Taricco on half-way and playing a one-two with Solskjaer before arrowing his effort across Keller but, again, a fraction wide.
The breakthrough finally arrived after 67 minutes. It was a disappointing goal from our point of view as Toda's pass was intercepted on United's 18-yard line, the visitors broke, Beckham's raking pass was flicked on by Scholes to Giggs and his cross met by Scholes, who couldn't miss from six yards.
Play became a little scrappy as substitutes entered the fray but the next chance was ours after 83 minutes - Poyet's header from Carr's wicked free-kick flashed inches wide with Carroll rooted to the spot.
With space opening up, the second goal was no surprise. Substitute Quinton Fortune broke quickly from the left, his cross found Van Nistelrooy and the striker finally bagged his goal witha clinical finish from eight yards.
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20secs: SAVE. Van Nistelrooy onto long ball, into box, shot forced sharp early save from Keller.
4mins: Swift move with Scholes and Keane creating opening for Giggs, straight at Keller from 18 yards.
5mins: Davies found in space right-hand side of box, hit volley across goal, no-one there to capitalise.
6mins: Superb control by Robbie Keane took him into box, last-ditch tackle by Roy Keane cleared danger.
10mins: Keller out of his box to clear as Beckham aims for Giggs over the top.
11mins: Sheringham found Etherington bursting into the box, Carroll out bravely to save at his feet.
15mins: CLOSE. Etherington free-kick met by Richards' flick header that sailed a yard wide.
20mins: CHANCE. Quick break involving Giggs, Beckham and Scholes ended with Van Nistelrooy poking Giggs' low cross wide from close range.
25mins: Decent spell of possession ended with Poyet's 20-yarder saved comfortably by Carroll.
29mins: SAVE. Ball squeezed under King's foot to Van Nistelrooy, clear in box, superb reaction save from Keller to take pace off ball, Taricco completed clearance.
30mins: SUB. Gardner for injured Richards.
31mins: SAVE. Beckham's cross met by Van Nistelrooy, eight yards out, tipped over by Keller.
38mins: SAVE. Keane fizzed pass into Van Nistelrooy, superb turn opened up one-on-one chance, Keller out to save at his feet.
40mins: Keane wriggled away from Brown, attempted cross cut out by Carroll.
44mins: More good possession eventually created chance for Carr bursting into box, looked to cut back on his right foot and tackled by Solskjaer.
Half-time: Spurs 0-0 United
47mins: SAVE. Keller tipped over Solskjaer's drive.
51mins: Superb block from King to deny Solskjaer from 20 yards.
53mins: Another great block, this time Gardner to deny Giggs.
54mins: SUB. G Neville for Brown.
57mins: Van Nistelrooy looping header floated wide.
58mins: King volley from 22 yards sailed over.
60mins: CLOSE. Giggs low drive across goal inches wide.
65mins: CLOSE. Van Nistelrooy spun away from Taricco, one-two with Solskjaer, into the box but fired across Keller and a fraction wide.
67mins: GOAL. All stemmed from our attack, Toda pass intercepted, Beckham raking pass flicked on by Scholes to Giggs, his cross met by Scholes, couldn't miss from six yards. 0-1.
71mins: SUB. Fortune for Solskjaer.
77mins: SUBS. Iversen and Bunjevcevic for Toda and Etherington.
83mins: CLOSE. Carr whipped in free-kick from left, Poyet's flick inches wide with Carroll stranded.
89mins: SAVE. Sliced clearance from Gardner fell to Giggs, full volley from 10 yards, Keller saved low to his right.
Injury time: Quick break by Fortune, squared to Van Nistelrooy, clinical finish from eight yards. 0-2.
Line-ups: Spurs: Keller, Carr, Taricco, King, Richards (Gardner, 30), Poyet, Toda (Bunjevcevic, 77), Davies, Etherington (Iversen, 77), Sheringham, Keane. Subs: Sullivan, Acimovic.
United: Carroll, O'Shea, Brown (G Neville, 54), Ferdinand, Silvestre, Beckham, Keane, Scholes (Fortune, 71), Giggs, Van Nistelrooy, Solskjaer. Subs: Ricardo, Blanc, Forlan.
Paul Scholes and Ruud Van Nistelrooy finally ended Kasey Keller's resistance as United took a huge step towards the title at the Lane.