Somdev, seeded 27, made short work of local teen James Duckworth 6-2, 6-1 in the first round of the men's singles qualifying draw.
In contrast, Amritraj came from behind to beat Germany's Andre Begemann 4-6, 6-1, 6-3 to advance to the second round. However, Yuki Bhambri frittered away a strong start to lose his opening encounter 6-3, 3-6, 3-6 to Jan Minar of Czech Republic.
Somdev will next take on Germany's Tobias Kamke while Amritraj will clash with French 25th seed Edouard Roger-Vasselin.
The main draw competition will begin from Monday.