The Indian ace was leading 5-2 in the first set after the two players traded breaks of serve. A spurt of unforced errors from Sania's racquet then allowed Dementieva to win the next four games and make it 6-5.
The 19-year-old Indian then won the 12th game with an ace and pushed the set into the tie-breaker.
Sania was 5-4 up in the shootout before she put a backhand wide and the Russian followed it up with a forehand winner to go 6-5 up.
A Sania forehand then went just wide to give the set to Dementieva.
In the second set, the Hyderabadi teenager saved two break points in the very first game but could not stop her opponent from gaining a 3-2 lead. She then fought back to level the scores at 4-4.
A tiring Sania then sprayed her shots to lose serve once more and went down 4-5. But Sania kept fighting as she forced three break points when Dementieva served for the match and converted the third when her rival hit a forehand long.
But Dementieva hit back to force two break points of her own and went up 6-5. Dementieva then made no mistakes when she served for the match for the second time and won the tie after one hour and 25 minutes.