The 23rd seed Sania came back well from a one-set deficit but failed to continue with the momentum and lost 1-6, 6-3, 3-6 in the second and final qualifying round of the US $2 million WTA event on Sunday night.
Earlier, Heidi, ranked 194 in WTA charts, had shocked top seed and world number 35 Anastasia Avlyuchenkova in the first round.
Heidi broke Sania twice in the first set to race away with the first set but the 74-ranked Indian got her act together and returned the compliment thrice in the second set apart from saving three break-points to draw level.
However, in the decisive third set, Sania could not convert any of the five chances to break Heidi, who converted her only chance to close the game in her favour.