Williams lost 6-1, 6-3 to the 79th-ranked Russian in what was the 32-year-old's first opening round loss at the All England Club since her 1997 bow.
Defeat for the American star, unseeded for the first time since that debut year, will also cast further doubts over her future in the sport.
She arrived at Wimbledon desperately short of fitness and confidence with a world ranking down at 58 following a six-month absence from the tour suffering from Sjogren's Syndrome, which causes joint pain and fatigue.
Monday's defeat was just her fourth loss at the first round stage of a Grand Slam against 52 wins and it also followed a dispiriting second round exit at the French Open.
Williams, the 2000, 2001, 2005, 2007 and 2008 Wimbledon champion, was beaten in the quarter-finals in 2010 and fourth round in 2011, both times falling to Tsvetana Pironkova of Bulgaria in straight sets.
Vesnina, who had lost in the first round of nine of her last 10 Grand Slam apperances, will face Polish third seed Agnieszka Radwanska for a place in the last 32.
Latest results on the first day of Wimbledon at the All England Club on Monday (x denotes seeding):
Men
First round
Novak Djokovic (SRB x1) bt Juan Carlos Ferrero (ESP) 6-3, 6-3, 6-1
Ruben Bemelmans (BEL) bt Carlos Berlocq (ARG) 7-5, 6-7 (4/7), 6-3, 7-6 (7/2)
Richard Gasquet (FRA x18) bt Tobias Kamke (GER) 6-2, 6-2, 6-2
Michael Russell (USA) bt Adrin Menndez (ESP) 6-3, 6-1, 7-6 (9/7)
Julien Benneteau (FRA x29) bt Gilles Muller (LUX) 6-2, 7-5, 7-6 (7/4)
Fernando Verdasco (ESP x17) bt Yeu-Tzuoo Wang (TPE) 7-6 (7/3), 6-4, 7-5
Mikhail Youzhny (RUS x26) bt Donald Young (USA) 4-6, 6-3, 6-2, 6-3
Ryan Sweeting (USA) bt Potito Starace (ITA) 6-2, 2-0 - retired
Women
First round
Su-Wei Hsieh (TPE) bt Virginie Razzano (FRA) 6-2, 6-4
Sabine Lisicki (GER x15) bt Petra Martic (CRO) 6-4, 6-2
Andrea Hlavckov (CZE) bt Kai-Chen Chang (TPE) 6-1, 6-2
Agnieszka Radwanska (POL x3) bt Magdalna Rybrikov (SVK) 6-3, 6-3
Elena Vesnina (RUS) bt Venus Williams (USA) 6-1, 6-3
Anna Tatishvili (GEO) bt Tamarine Tanasugarn (THA) 6-4, 6-2
Camila Giorgi (ITA) bt Flavia Pennetta (ITA x16) 6-4, 6-3
Li Na (CHN x11) bt Ksenia Pervak (KAZ) 6-3, 6-1
Sorana Cirstea (ROM) bt Pauline Parmentier (FRA) 6-4, 6-1
Ayumi Morita (JPN) bt Jarmila Gajdosova (AUS) 6-4, 6-3
Arantxa Rus (NED) bt Misaki Doi (JPN) 7-5, 6-3
Samantha Stosur (AUS x5) bt Carla Surez (ESP) 6-1, 6-3