Williams, who is unseeded, needed only 68 minutes to beat Bencic 6-3 6-1, who is co-coached by Martina Hingis' mother and coach Melanie Molitor, to set up a meeting with ninth seed Mona Barthel in the second round.
Better days are sure to come from Bencic though – the teenager is ranked 619 in the world after winning back-to-back ITF titles recently and has already represented Switzerland at full Fed Cup level.
The top three seeds in the event all safely made their way into the second round.
Top seed Roberta Vinci had the biggest scare as she dropped a set in between two bagels against Olga Govortsova – winning 6-0 2-6 6-0.
The Italian could potentially take on Anne Keothavong next. The British player is in the main draw as a lucky loser and will play Kiki Bertens of the Netherlands in the first round.
Second seed Julia Goerges kept up the form that got her to the WTA Linz final last week with a 6-2 6-1 win over Silvia Soler Espinosa.
While former world number one and third seed Jelena Jankovic only had to play three games against China's Shuai Peng before her opponent had to retire with a right shoulder injury.
In Moscow, Defending champion Dominika Cibulkova beat Russia’s Ekaterina Makarova 2-6 6-4 6-2 to reach the second round of the Kremlin Cup.
The fifth seed, who won her second career WTA Tour title at Carlsbad earlier this year, recovered from a set down to beat the world number 20 with a fine display in the deciding set.
Cibulkova will next take on Bulgaria’s Tsvetana Pironkova in the second round.
Sixth seed and home favourite Nadia Petrova was beaten 3-6 7-5 7-5 by Simona Halep of Romania.
WTA Luxembourg results
Venus Williams (U.S.) beat Belinda Bencic (Switzerland) 6-3 6-1
Lourdes Dominguez Lino (Spain) beat Tatjana Malek (Germany) 7-6(3) 6-1
2-Julia Goerges (Germany) beat Silvia Soler Espinosa (Spain) 6-2 6-1
Annika Beck (Germany) beat Barbora Zahlavova Strycova (Czech Republic) 5-7 7-6(2) 6-2
1-Roberta Vinci (Italy) beat Olga Govortsova (Belarus) 6-0 2-6 6-0
3-Jelena Jankovic (Serbia) beat Peng Shuai (China) 3-0 (Peng S retired)
6-Sorana Cirstea (Romania) beat Petra Martic (Croatia) 6-2 6-2
WTA Moscow results
Simona Halep (Romania) beat 6-Nadia Petrova (Russia) 3-6 7-5 7-5
Alize Cornet (France) beat Anastasia Rodionova (Australia) 6-4 6-3
Yaroslava Shvedova (Kazakhstan) beat Anastasia Pavlyuchenkova (Russia) 6-2 6-2
5-Dominika Cibulkova (Slovakia) beat Ekaterina Makarova (Russia) 2-6 6-4 6-2
Vesna Dolonc (Serbia) beat Galina Voskoboeva (Kazakhstan) 1-6 6-1 6-4
Tsvetana Pironkova (Bulgaria) beat Varvara Lepchenko (U.S.) 6-0 7-6(3)
- Olga Govortsova