Norwich went into the clash second and on the back of an eight-match unbeaten run in the league, but it proved a frustrating fixture at a packed Carrow Road for Alex Neil's side, with an Alex Tettey own goal the difference.
After Patrick Bamford saw his low cross sliced behind for a corner in the eighth minute, Tettey accidentally diverted the resulting set-piece beyond the helpless John Ruddy to give Middlesbrough the lead.
Despite controlling proceedings for the majority of the match, Norwich found clear-cut chances hard to come by, while Bamford tested Ruddy at the start of the second period.
Lee Tomlin then went close with a rasping drive from 25 yards in the 72nd minute, before a crucial Ben Gibson block in the second minute of stoppage time denied Russell Martin a late leveller.
Middlesbrough are a point clear of Bournemouth and two ahead of Watford.
In League One, second-placed Preston North End were to a 2-2 draw by 10-man Port Vale.
Daniel Johnson put Preston ahead after 12 minutes, but Michael O'Connor eventually restored parity early in the second period via a penalty.
A Richard Duffy red card for handball inside the area seven minutes later allowed Joe Garner to convert a penalty of his own, though the day's third spot-kick ultimately cost Preston two points five minutes from time.
John Welsh brought O'Connor down and the midfielder slotted away his second of the day, securing a draw for Vale and leaving Preston four points ahead of third-placed MK Dons.
