The French giants went through 5-1 on aggregate after emphatically adding to their 1-0 win in Poland.
Marc Planus opened the scoring on 41 minutes before Marouane Chamakh doubled their advantage just a minute later.
Ivan Krizanac then put through his own net to make it 3-0, before Albert Riera (pictured) scored from the penalty spot with just 16 minutes left.
Bordeaux's evening was soured by the sending off of Kodjo Afanou with just a few minutes remainng.
Groclin sealed a consolation in the final minute when Tomasz Wieszczycki pounced.
Auxerre booked their place in the next round of the Uefa Cup with a very good 1-0 success in Athens against Panathinaikos.
After a goalless draw in France the Greeks were fancied to seal a place in the next round, but it was Auxerre who shocked their opponents.
Former Feyenoord star Bonaventure Kalou grabbed the only goal after 71 minutes to send his side through.
French giants Marseille progressed into the fourth round of the Uefa Cup with a 0-0 draw with Dnipro in Ukraine.
Marseille had a 1-0 advantage from the first leg in France, but knew they faced a tough trip to the Eastern European outfit.
However, Jose Anigo's side managed to hold tight and play out a goalless draw which gives them passage into the next phase.
Internazionale moved into the fourth round of the Uefa Cup on away goals after they were held to a 0-0 draw by Sochaux at The Giuseppe Meazza.
After drawing 2-2 in France in the first leg, Inter always had the advantage - but they could not create a clear lead as Sochaux battled hard.
Inter were even forced to finish the game with ten players as Christian Vieiri was sent off with four minutes remaining.
Bordeaux 4-1 Groclin (5-1 agg)
Dnipro 0-0 Marseille (0-1 agg)
Internazionale 0-0 Sochaux (2-2 agg - Inter through on away goals)
Panathinaikos 0-1 Auxerre (0-1 agg)
