The Magpies went ahead through their veteran striker’s tap-in, Henrique’s own goal doubled the scoreline just before half-time, before the Magpies No.9 capped off the evening
The Magpies took the lead with the first half exiting its infancy, Shola Ameobi tapping in from Gabriel Obertan’s hard work before - with half-time looming - Les Girondins centre-back Henrique doubled the opposition’s advantage by turning the ball into his own net.
The second half began with a third goal, this time from Papiss Cisse, leaving the result all but confirmed.
The three points allow Newcastle to boost up to four points in Group D with two Club Brugge ties on the horizon, while Bordeaux stay rooted on three points after their first competitive defeat since April 8 - a run of 18 matches.
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Magpies manager Alan Pardew made seven changes to his squad with one eye on the Manchester United encounter at the weekend, but his line-up was still a strong one featuring the likes of Papiss Cisse, Yohan Cabaye and Cheikh Tiote.
Cabaye fizzed an early effort just wide to set a bubbling tempo at the Sports Direct Arena while, at the other end, his opposition number, Ludovic Obraniak, skimmed a header a few feet over.
On 16 minutes, Gabriel Obertan started to steal the show, delicately bringing the ball down on the left, charging into the box and squaring across the face of goal for stand-in captain Shola Ameobi to give the hosts the lead with a tap-in from one yard.
The Tyneside club made the mistake of dropping deep to protect their lead immediately afterwards and, as a result, had to head clear a barrage of crosses and block countless shots.
However, with five minutes until half-time, Henrique flung himself at right-back Danny Simpson’s cross, turning it past his own goalkeeper Cedric Carrasso to compound the visitors’ misery.
The second half began similarly, despite the Ligue 1 club’s coach Francis Gillot making a double change. Papiss Cisse scored his second strike in three Newcastle matches, heading in Shane Ferguson’s cross although there was more than just a hint of offside about the goal.
Pardew brought on Gael Bigirimana and Dan Gosling to ensure their midfield became more defensive-minded and mobile while Les Girondins pressed on to try and salvage some pride.
But the Newcastle back-four remained impressive throughout and kept their second clean sheet in as many Europa League home matches this season, and their third out of four altogether.
Substitute goalkeeper Steve Harper - brought on at half-time after Rob Elliot had supposedly picked up a knock - had to stretch his legs to deny an unmarked Jussie a goal as the Magpies sat back and soaked up the Bordeaux dominance without a problem.