Typically for a Tony Pulis side, Boro's set-piece prowess was to the fore as Martin Braithwaite and then Aden Flint were the beneficiaries of Lewis Wing corners from the left.
Club stalwart Stewart Downing then converted Ryan Shotton's cross at the back post in the 25th minute to leave United with a thankless task.
By contrast, everything was up for grabs in the closing stages at the City Ground as West Brom battled to a 1-1 draw with Nottingham Forest.
The game failed to catch fire early on but Adlene Guedioura arrowed home a fine long-range strike for the hosts shortly before the hour.
West Brom left it until three minutes from time to level matters when Matt Phillips crashed a brilliant effort into the roof of the net and Harvey Barnes looped a cross against the Forest bar amid a breathless finale.