Showing supreme movement and clinical ball-striking, Andreeva breezed through the opening set in 31 minutes.
Baptiste, ranked 55th in the world, was willed on in the second set by an enthusiastic crowd who wanted to see a true contest.
When Andreeva broke for a 3-1 lead, the result looked a formality. Baptiste instantly broke back to halt Andreeva’s progress but lost serve again as the world number seven secured a straightforward win in one hour and 18 minutes.
Under the tutelage of former SW19 champion Conchita Martinez, she has already won two WTA 1,000 titles – the rung of tournaments below the majors – in Dubai and Indian Wells this season.
Her impressive progress is demonstrated by the fact she has won 35 tour-level main-draw matches this year – a tally only bettered by world number one Aryna Sabalenka (44) and five-time major winner Iga Swiatek (37).
A much tougher test than 23-year-old Baptiste awaits Andreeva next, however.
Reigning champion Barbora Krejcikova of the Czech Republic and American 10th seed Emma Navarro meet later on Saturday for the right to face her.