Vladimir Dyadyun had stunned the Stade de Gerland as he handed the Russian visitors a third-minute lead, but Bafetimbi Gomis led the Lyon response, by scoring one and creating another to give Remi Garde's side the lead before Briand sealed the win in a refreshingly open contest.
"It gives me pleasure to have scored," said Briand.
"I am happy to have given the team a two goal advantage. That is already a good thing.
"Now, we are going to try and wrap it up in Russia. I had learnt from previous corners to get in front of the first defender.
"I gave it a go and it left me with a smile on my face."
Lyon are bidding to reach the group stages of Europe's elite club competition for the 12th consecutive season, but Garde's men came into this tie on the back of a frustrating draw against unfancied Ajaccio in Ligue 1 on Saturday.
Meanwhile Rubin made the long trip from Tatarstan with two-thirds of their domestic season already completed.
They lie fourth in the Russian Premier League, and they looked well-placed to return to the Champions League group stage for a third straight season when Dyadyun turned in Bebras Natcho's right-wing corner.
From a Lyon point of view, the goal might have been avoided had Hugo Lloris deployed a defender on his far post, but they never panicked, and were back level with ten minutes on the clock.
Gomis got in between two Rubin defenders to apply an excellent first-time finish to a Michel Bastos cross, and Briand might then have put the hosts in front with a lob that 'keeper Sergei Ryzhikov did well to save.
However, they were not to be denied for long, with Kim Kallstrom and Lisandro Lopez combining to set up Gomis five minutes before half-time, his cross-cum-shot from the left taking a decisive touch off Saba Kvirkvelia on its way into the net.
Rubin were set up in a cautious-looking 5-4-1 formation, but the chances continued to flow after the restart, as Ryzhikov almost let a Bastos cross past him before Gokdeniz Karadeniz saw his powerful shot turned over the bar by Lloris.
Former Rennes striker Briand then glanced home a Kallstrom corner to give Lyon a vital two-goal cushion, and while Bastos somehow failed to convert a Gomis pass with the goal gaping late on, Garde can be delighted with his side's powers of recovery.
With the second-leg to come in Russia next week, the tie is still far from over, but Lyon are firmly in the driving seat.
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