The Indian had little trouble bagging the first set but was stretched in the second, and her rival continued to do that in the next two sets as well.
In the third set, Sreeja and Kallberg went neck-to-neck till 7-5, but the Indian found her bearings just in time to pocket it.
Sreeja made the early running in the fourth set, taking a 9-3 lead, but a few unforced errors and a couple of good smashes helped Kallberg narrow the lead to 9-7 and then to 10-8.
But a powerful unanswered forehand to the right corner of the table propelled Sreeja to the next round.
In the other matches of the day, Manika Batra will face Anna Hursey of Great Britain while veteran