Patrick Bamford scored his first ever senior hat-trick to secure the points for a team that have now won three of their last five league fixtures. Leeds, meanwhile, failed to build on their 1-0 victory over Brentford last time out as the Whites stayed down in 11th position in the table.
Leeds's first opportunity arrived in the 13th minute when the ball broke for Samuel Saiz in a dangerous area, although the attacker's effort was never threatening to test Boro goalkeeper Darren Randolph.
Both teams were having moments in the final third, but it was the hosts that took the lead in the 31st minute when Bamford expertly turned a dangerous Downing cross into the bottom corner of the net.
Bamford also had the first opportunity of the second period when Leeds goalkeeper Wiedewald made a mess of a long throw from Shotton, but the striker's effort was deflected wide of the post.
Pierre-Michel Lasogga had Leeds's first attempt of the second half in the 66th minute, but the striker's effort was always too high.
Less than two minutes later, Bamford completed his hat-trick as the 24-year-old found the bottom corner from close range after Traore's strike had been deflected into his path.
Former Barcelona youngster Traore continued to dazzle the Riverside with his skill in the latter stages, but Boro could not find a fourth despite a couple of half-chances.
MIDDLESBROUGH (4-3-3): Randolph; Shotton, Ayala, Gibson, Friend; Howson, Leadbitter (Clayton 44'), Besic; Downing, Bamford (Cranie 90'), Traore
LEEDS (4-2-3-1): Wiedwald; Berardi, Jansson, Cooper, Anita; O'Kane (Ekuban 69'), Phillips (Vieira 46'); Dallas, Saiz, Alioski (Forshaw 46'); Lasogga