Conti had threatened early on, hitting the bar and forcing Siobhan Chamberlain to tip another effort round the post, the keeper also turning an Elena Danilova shot over.
Helen Bleazard fired over from a great position for Bristol and after Jess Fishlock's shot was parried, Ann-Marie Heatherson cleared the bar.
Lillie Billson set up Fishlock to net the hosts the lead but Jemma Rose was sent-off for handball on the line and Conti converted.
Bristol did survive a second penalty claim though and still had another scare as Veronica Boquete was denied by the bar.
The second leg takes place on October 5th at the Centralni Stadium, Voronezh, kick-off 5pm (CET).
Bristol Academy: Siobhan Chamberlain, Grace McCatty, Jaz Matthews, Corinne Yorston, Jemma Rose, Michelle Green (Katie Daley, 63), Helen Bleazard (Alex Culvin, 88), Anouk Hoogendijk, Ann-Marie Heatherson (Lillie Billson, 69), Jessica Fishlock, Loren Dykes.
Unused Subs - Alex Windell, Rachel Simkin, Jade Radburn, Ellie Curson.
Energiya Voronezh: Veronica Shulga, Anna Astapenko, Augustine Siliki, Anastasia Kostyukova, Olesya Mashina, Yulia Zapotichnaya, Veronica Boquete (Marina Saenko, 90), Pamela Conti, Elena Danilova, Elena Terekhova (Nadezda Bosikova, 45), Ajara Njoya (Kristina Chichkala, 78).
Unused Subs - Adriana Parente, Erika Prado, Nana Gelbakhiani, Lyudmila Tsukanova.
Photos - tgsphoto.co.uk
She Kicks - the online news service for women's football