A tense game with little in the way of quality was separated by a David de Gea goal kick, Romelu Lukaku flick on and finish from the substitute nine minutes from time.
Spurs stay in third, a position they cannot move down from no matter the other weekend results, but United now boast 22 points after 10 games.
A busy Saturday schedule continues from 3pm with City afforded the chance to restore their five-point advantage at West Brom with Arsenal also in action against Swansea City at Emirates Stadium.
EPL Table | Premier League 2017-18 season table
Crystal Palace host West Ham in Saturday’s London derby at Selhurst Park as both sides scrap for points at the bottom of the table, while Watford face stoke City hoping to climb into the top four after a great start under Marco Silva.
Jurgen Klopp desperately needs a win against his protege David Wagner as Huddersfield travel to Anfield to face Liverpool, while champions Chelsea take on Bournemouth on the south coast in Saturday’s late kick-off.
In Sunday’s action, Brighton host Southampton before Everton travel to Leicester after both sides recently sacked their managers.
Burnley host Newcastle United to complete the weekend’s action on Monday night.