The Brazilian defender was shown a second yellow after tripping Benoit Assou-Ekotto to set up a nervous finale to an open attacking match.
Spurs, though, could not find the goal that would have given them their first win over United in 10 years and the point kept them fifth, on 37 points.
United's eighth draw in 10 away matches took them top on 45 points from 21 games, ahead on goal difference of Manchester City, who have played two games more. Arsenal are third on 43, with Chelsea fourth on 38.
News that makes sense
Your trusted source for staying up-to-date with the world around you. Get free daily news updates and analysis, straight to your inbox.
The day's three Premier League derbies all finished in draws. Liverpool were held 2-2 at Anfield by Everton, Sunderland scored late to snatch a 1-1 home draw with Newcastle United and Birmingham City against Aston Villa also ended 1-1.
