Sixth seed Somdev beat Ginepri 7-6 (4), 2-6, 6-2 after a two hours contest.
After winning the first set in tie-break, Somdev had three break opportunities in the second but could convert none. He dropped his serve twice as Ginepri made a comeback.
Somdev did not repeat that mistake in the third set as he cashed in on three of the four chances to move to the third round.
It was second meeting between Somdev and Ginepri and now the head-to-head score is 1-1.
He now faces Briton James Ward and a win will book him a berth in the main draw of the last Grand Slam of the season.
Somdev, ranked 113 and James, ranked 173 have never played against each other.