The sixth-seeded American cruised past a player who is on the comeback trail after missing nine months because of various reasons. Groenefeld did reach the fourth round of the U.S. Open but she was no match for the power and precision of the elder Williams sister.
"She hit some great shots but my experience helped me,'' said Williams, who made it into the second round in 1998 in her only previous appearance in Stuttgart.
Williams needed four set points to close out the first set, committing a double-fault on one of them.
The American then broke serve for 1-0 at love to start the second. She went two breaks up to lead 4-1, allowed the German one more game and hit a forehand winner on her second match point.
Williams next plays qualifier Kateryna Bondarenko, who rallied to upset 15th-ranked Flavia Pennetta 4-6, 6-2, 6-1.
Eight-seeded Agnieszka Radwanska swept past Sandra Zahlavova 6-3, 6-2.
Another qualifier also advanced when Tsvetana Pironkova beat teenager Alize Cornet of France 6-2, 6-1. The Bulgarian next plays third-seeded Dinara Safina of Russia, who had a bye into the second round, along with the other top three players in the tournament - Serena Williams, Jelena Jankovic and Elena Dementieva.
Marion Bartoli of France advanced by beating Dominika Cibulkova of Slovakia 6-3, 6-1, and Victoria Azarenka wasted a 5-2 lead before overcoming Agnes Szavay 7-5, 6-3 to set up a second-round contest against Radwanska.
The indoor tournament has brought together eight of the top 10 players in the world, with only Ana Ivanovic and Maria Sharapova missing.
Serena Williams, who regained the No. 1 ranking after winning the U.S. Open, plays Wednesday against Li Na.
Williams' closest rival to finish the year as No. 1 is Jankovic, who trails by 21 points. Jankovic, who won the China Open on Sunday, will not play until Thursday, when she meets Alona Bondarenko, Kateryna's sister.
Sporting Injury Worries Lessen
Bondarenko upsets Pennetta
Serena returns for first time since U.S. Open
La Liga Team Of The Week: Round 2
