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Obertan's 48th-minute strike gave Newcastle a deserved lead and while Brugge dominated the rest of the action, they could not find an equalising goal.
Former Manchester United winger Obertan ended the stalemate soon after the interval by firing in from the right edge of the penalty area following Sammy Ameobi's pass.
Brugge seemed to be ignited by Newcastle's opener and immediately launched a succession of attacks on Steve Harper's goal.
However, some wasteful finishing cost the Belgians a point as they squandered numerous equalising chances.
Striker Carlos Bacca was the chief culprit, heading over from six yards after being found unmarked in the box.
The Colombian had previously tested Harper with a stinging low shot, while the Magpies stopper was also called into action to deny Lior Rafaelov.
Newcastle themselves had chances to make their lead more comfortable, but both Ameobi and Shane Ferguson were off-target with their efforts.
Pardew brought captain Fabricio Coloccini off the bench, and his introduction helped the hosts sure things up in defence and hang on for the points.