"The timing of the second goal was very important," said Middlesbrough winger Stewart Downing. "We defended well throughout the team but are disappointed we conceded.
"Not many players in our team have played much in the Premier League. It was a team effort today."
Stuani opened the scoring with a piece of individual brilliance after 12 minutes, firing a long-range shot from outside the area over the head of goalkeeper Vito Mannone.
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Then, just before the interval, the 29-year-old rounded off a well-worked team goal after Adam Forshaw combined with Alvaro Negredo to split the home defence open.
Sunderland, who lost central defender John O'Shea to injury in the first half, refused to buckle and fully deserved their goal when Van Aanholt struck from inside the area after keeper Brad Guzan could only parry a shot from Duncan Watmore.
But they could not prise Boro open again and David Moyes's side, who featured all three of their new signings from Manchester United, remain without a point after two games while Middlesbrough have four from their opening matches.
Van Aanholt refused to be downhearted. "I think the way we played in the second half, (we) should not be scared of anyone," said the Dutchman. "The season has just started I am very positive we are capable of winning games."
(Reporting by Neil Robinson; editing by Ken Ferris and Brian Homewood)
