Alexandre Lacazette and Corentin Tolisso had their efforts saved in the shootout after the match had ended in a 2-2 draw on Wednesday.
"We play football for this," goalkeeper Ronan Jay told broadcaster beIN Sports. "It will stay with us for life, it's unbelievable."
Less than 50 kilometres separate the two cities, but the clubs have little in common.Â
Lyon are one of the most storied in French soccer, having won the league title seven times to add to five Cup titles, while Bourgoin-Jallieu play in the fifth division.
Mehdi Moujetzky scored both goals for Bourgoin-Jallieu, giving his team an early 1-0 lead and levelling the scores at 2-2 in the 69th minute after Georges Mikautadze put Lyon ahead. Nemanja Matic had scored Lyon's opener.
Moujetzky missed his penalty in the shootout but that did not prevent Bourgoin-Jallieu from sealing the historic result.
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Meanwhile, Paris St Germain booked their place in the last 16 with a hard-fought 4-2 victory over fifth-tier side FC Espaly.
Espaly sprang an early surprise when Kevis Gjeci capitalised on a mistake by Arnau Tenas to score inside three minutes.Â
PSG dominated but could not find the breakthrough until Warren Zaire-Emery equalised in the 37th minute.
Espaly goalkeeper Jordan Etienne put in an impressive performance after the break but was unable to prevent Desire Doue from scoring in the 67th minute.Â
The hosts pulled one back four minutes later through Maxence Fournel.
PSG, determined to find a winner, continued to attack and with two minutes remaining Bradley Barcola was on hand to head home Nuno Mendes' cross.Â
Goncalo Ramos added the icing on the cake with a penalty in stoppage time.Â