Boulter won a tough opening set against an inspired Zakharova before running away in the second set to win 6-4 6-0 and faces China’s sixth seed Yue Yuan in the last four.
The British number one, who reached the semi-finals in Tokyo last week, raised her level when it mattered against a 113th-ranked opponent who matched the second seed for most of the first set.
But Boulter held serve with an ace to lead 5-4 and then sealed the first break of the match to take it 6-4 after Zakharova hit a forehand into the net.
Zakharova put the world number 29 under pressure in the opening game of the second set, but Boulter held and then fired a superb volley at break point to lead 2-0.
A second break followed for the Brit thanks to a stunning forehand at the crossroads as she raced to a 4-0 lead and, after holding once more, she broke Zakharova for a third time to wrap up the victory in one hour and 16 minutes.