Lyon reach Women's Champions League last eight despite Brann draw
France midfielder Amel Majri and Norway attacker Aga Hegerberg, with a penalty, had put the record eight-time winners 2-0 up after just 13 minutes.
Justine Kielland cut the deficit for the home side 10 minutes before the break in snowy Bergen.
Lyon played most of the second half a player down as USA international Lindsey Horan was shown a red card before Brann claimed a dramatic equaliser in stoppage time.
Defender Marit Lund delivered a corner before Lyon goalkeeper Christiane Endler fumbled and 18-year-old Brann midfielder Signe Gaupset volleyed home the crucial goal.
"I'm disappointed for the players," Lyon coach Sonia Bompastor said.
"I would have liked them to be rewarded with a better result."
"We will wait to be sure of top spot and we will have to win one of the two remaining matches," she added.
Brann are second in the table, with a six-point advantage over the other two teams in Group B, Slavia Prague and St Poelten.
Their game was postponed after 14 people were killed in a shooting in the Czech capital earlier in the day.
In Group A, Eintracht Frankfurt's Laura Freigang missed a 90th-minute penalty as the German outfit drew 1-1 with Benfica, keeping both sides' chances of reaching the knock-out stages alive.
Holders Barcelona host Sweden's Rosengrad later looking to book their last-eight spot with a win.
On Wednesday, Australia's Sam Kerr netted in Chelsea's 3-1 win at Swedish club Hacken, while Real Madrid's hopes of reaching the quarter-finals were ended in a 1-0 home loss to Paris FC.