Garcia, seeded second, recovered to see off the Bulgarian 6-7 (2-7) 6-2 6-4 in the WTA Premier event in New Haven.
Earlier, Konta pulled out of the tournament due to a viral illness, affording Carla Suarez Navarro a walkover route into the quarter-finals.
Halep and Bertens, the finalists at last week's Cincinnati Masters, had already announced their intention not to feature on the outdoor hard courts in Yale.
The Romanian world number one, surprisingly beaten by Bertens in the Cincinnati decider, cited a right Achilles problem that could leave her in doubt for the US Open as the reason for her withdrawal, while Bertens, like Konta, is suffering from a virus.
Belinda Bencic, the lucky loser who benefitted from Halep's absence, defeated Camilla Giorgi is straight sets. Anett Kontaveit ousted Bertens' replacement Pauline Parmentier 3-6 6-2 6-2.
In the final match of the day, Julia Goerges was made to work hard by Dayana Yastremska, the fifth seed ultimately prevailing 6-3 3-6 6-4.