Remi Garde's men progressed into the quarter-finals of the Coupe de France at the expense of les Girondins with two goals in extra time
Jussie had put the three-time winners ahead in the first half after a defensive mistake allowed him slot home the opener. Despite numerous chances, the hosts responded well and equalised soon after through Alexandre Lacazette.
World-class saves from Cedric Carrasso came to Bordeaux's rescue on more than one occasion as the visitors struggled to keep up. However, for all of les Gones' profligacy in front of goal, they would take the lead in the 96th minute through substitute Bafetimbi Gomis before Jimmy Briand netted in the 118th minute to seal victory.
Remi Garde made six changes from the side which drew against Marseille in the league on Sunday, with the likes of Gueida Fofana and Yoann Gourcuff given starting berths against a Bordeaux side who were yet to taste defeat in the calendar year.
After a slow start, it was les Girondins who raced out of the traps on a chilly day in Lyon.
Gourcuff proved to be too elaborate in his bid to evade his marker and Francis Gillot's men countered with impressive speed. Yoan Gouffran was then able to pick out Jussie, who launched a powerful effort past Hugo Lloris.
Gourcuff almost atoned for his mistake four minutes later when a curling free kick zipped past Cedric Carrasso's post. At the other end, Jussie and Gouffran again proved to be a handful with the latter shooting wide past Lloris' post as the match opened up.
The hosts equalised in superb attacking fashion. Gourcuff was again in the mix of things as he elevated a lofted ball in the area towards Ederson whose first-time header was saved by Carrasso, with Lacazette scoring on the follow-up.
Lyon, last winners in 2008, were the better side early in the second half, and should have found the net on a number of occasions. Ederson ran a ball through to Lisandro Lopez who fired home, though the goal was chalked off for offside - a decision condemned by the sparse crowd inside the Gerland.
Moments later, the front three combined again to bamboozle the visitors' defence who were at sixes and sevens, though this time Lacazette's finish would be thwarted by a fine save by Carrasso.
The onslaught continued as Lisandro was found in acres of space once again and for the second time in mere minutes, the Argentine's goal was disallowed for offside as the visitors struggled for possession.
Bordeaux, aiming to win the competition for the first time since 1987, improved their attacking rhythm, and almost forced a goal as Gregory Sertic's effort was palmed away by Lloris. Carrasso was again producing heroics at the other end from Lacazette as the match descended into an end-to-end affair.
Five minutes from the end of normal time, Jussie latched on to a through ball behind the defence before being tugged down by Lyon captain Cris, who was only shown a yellow card by the referee, despite being the last defender.
Les Gones went ahead in the sixth minute of extra-time through substitute Gomis. The France international calmly slotted in after the ball fell to him on the edge of the six-yard box as Carrasso was finally beaten.
The game was subsequently made safe two minutes from the end of extra-time as Briand tapped in from Lisandro's low centre.