The Ukrainian hosts dominated the contest and took a deserved lead through Lukman Haruna, but that was cancelled out within minutes by Ludovic Obraniak.
Gusev then won his side a penalty which could have secured the win, but he hit the woodwork with his kick on a frustrating night at the Olimpiyskiy National Sports Complex.
Dynamo were making their season debut in the competition after dropping down from the Champions League, and were first to register a shot with a fantastic drive from Niko Kranjcar which brought the best out of goalkeeper Cedric Carasso after eight minutes.
The Croatia midfielder tried his luck again after 15 minutes but pushed his left-footed effort past the right post.
However, the Ukrainian hosts took a deserved lead five minutes later through Haruna, who latched on to a cross from Taye Taiwo and slammed the ball into the top right corner.
It was the wake-up call Bordeaux needed and three minutes later they were level when Obraniak curled in a low shot from Gregory Sertic's pass.
The match tempo rose after that and Andriy Yarmolenko had Dynamo's next chance but could only drill over the bar.
Obraniak did the same at the other end of the pitch but it was Haruna who came closest to scoring again five minutes before the interval, with a beautiful drive from 25 yards which deserved a better outcome than hitting the crossbar.
A frantic start to the second half produced shots off target from Haruna, Roman Bezus and Miguel Veloso as Dynamo looked to make an immediate impact.
Carasso then made another important save after 50 minutes, although he looked less than convincing when fumbling Kranjcar's curling left-footer.
Bordeaux were struggling to contain their opponents and Yarmolenko was twice denied by Carasso, much to the frustration of the home fans.
Their pressure finally came to something after 76 minutes, though, when Gusev won his side a penalty after hitting the deck under a challenge from Carlos Henrique.
However, Gusev failed to make the most of the opportunity, directing the resulting spot-kick on to the crossbar.
It was a welcome reprieve for Bordeaux and their luck held into stoppage time when Haruna saw a superb strike from distance cleared off the line by Marc Planus.