The 102-ranked Indian won 6-2 6-3 against his Australian rival, placed 64 in the ATP charts, in one hour and 13 minutes in the euro 485,760 clay court event.
The win is Somdev's first after suffering five straight first-round defeats in the last three months. The last time he won a singles match on the ATP tour was when he defeated Juan Martin del Potro in ATP 500 Dubai event in February.
Somdev broke Ebden early to take a 2-1 lead and raced away with the opening set. The second set was fought tightly as the two players were locked 3-3, but Somdev broke the Australian in the seventh game and one more time in the ninth to eke out a confidence-boosting win.