Tremoulinas whipped in another well-measured cross in the 11th minute, but Yoan Gouffran could only head it over the bar.
That came to haunt the French outfit as Newcastle went ahead in the 16th minute. Cabaye played a brilliant crossfield pass to Gabriel Obertan, who got the better of Filho Mariano to cross for Shola Ameobi to tap in from just yards out.
However, Alan Pardew's side struggled to maintain their initiative thereafter and allowed Bordeaux to press themselves on them.
Gouffran came close to equalising for the visitors in the 28th minute before Ludovic Sane tried his luck from distance but failed to get his shot past Robert Elliot on 38 minutes.
Much against the run of play, Newcastle doubled their advantage in the 40th minute when Henrique deflected Danny Simpson's cross into his own goal.