The Australian netted his third goal in two games to send the visitors into the next round of the Capital One Cup, with Martin O'Neill's side turning in an ineffectual display
Tony Mowbray's side came into this game off the back of four straight wins, and made it five thanks to a first-half finish from the Australian striker.
Adam Johnson has struggled for the hosts since his move from Manchester City but put in two fine early crosses to unnerve Boro, with Louis Saha having an early shot after the visitors failed to clear their lines.
While the Black Cats hit the ground running, Ishmael Miller should have found the net for the visitors after 12 minutes. The imposing striker was through after John O'Shea's unfortunate slip, but he could not control the ball and the chance was lost.
Controversy followed soon after as McDonald was booked by Phil Dowd for a dive after 15 minutes, and the striker almost found the net on the half hour, but rattled the bar with his strike from 25 yards.
If that was a warning sign, O'Neill's men didn't heed it as McDonald did indeed find the net after 39 minutes. Miller again caused problems for the home side, drilling in a low cross to the striker, and the Australian found a fine finish to beat Westwood for his third goal in two games.
Miller beat Jack Colback for the goal, who looked uncomfortable at left-back for the hosts - in contrast, George Friend and Seb Hines were imperious at the back for Middlesbrough, with Friend making driving runs down the left throughout.
O'Neill brought on James McClean to try and change the game for his side in the second half, with the ineffectual Saha being replaced, but Middlesbrough continued to hold firm after a solid first half display.
Stephane Sessegnon looked the sharpest player in red and white on his return to first-team football, but could not find a way through as Sunderland were once again frustrated in forward positions by local opposition.
If there were to be further goals then the away side looked more likely, with Miller tormenting the Premier League defence in the closing stages.
The defeat to the Championship side leaves Martin O'Neill with the more important task of ensuring Sunderland do not get sucked into a relegation battle this season after an indifferent opening to their Premier League campaign.