Eight-times winners under their former name of Olympique Lyonnais, Lyon will face Barcelona or Bayern Munich, who play their second leg in Spain on Sunday after last week's 1-1 draw.
Lyon started strongly and had an early goal from a set piece disallowed but took the lead when Melchie Dumornay was felled in the box by defender Lotte Wubben-Moy and a penalty was awarded after the referee reviewed the incident on video.
Wendie Renard scored from the spot at the second attempt after goalkeeper Daphne van Domselaar moved off her line to save the defender's first effort.
Kadidiatou Diani hooked home at the back post from a corner to make it 2-0 nine minutes before the break as Lyon took a 3-2 lead in the tie.
Having showed little of the fire and industry that saw them secure a 2-1 home win in the first leg, Arsenal then levelled in the 76th minute through Alessia Russo, who stole between two defenders to steer home Smilla Holmberg's cross.
The game looked to be heading for extra time until Brand latched onto a pass from Dumornay, scoring with a deft left-foot finish in the 86th to see her side through to their 12th Champions League final.
The showpiece match will take place in Oslo on May 23.