Following the opening round exits of the top two seeds, Alizé Cornet and Anastasia Pavlyuchenkova, Giorgi's potential path to a maiden WTA title had opened up invitingly, but her hopes were dashed by World No.236 Dabrowski, who made a mockery of her lowly ranking to triumph, 3-6, 6-3, 6-2.
Everything started off brightly enough for Giorgi, who rattled off four games in a row to take the opening set. Yet while the Italian's groundstrokes were finding their mark, the same could not be said about her serve.
A couple of double faults handed Dabrowski a break at the start of the second set and with it the belief that she could turn the tables. With her serve misfiring, suddenly doubt started to creep into the rest of Giorgi's game and when she netted a routine backhand the Canadian was level at one set all.
The double faults continued into the decider, Dabrowski capitalizing fully to surge into a 5-0 lead. Dabrowski had never previously won a WTA main draw match and she was forced to overcome a late wobble before eventually coming through to complete victory when Giorgi sent a forehand long.
"I thought I served well and better than I did in my two qualifying rounds, which I knew I had to do - she's so aggressive that I couldn't just roll my serve in," Dabrowski said. "She likes to have the match in her hands, so she goes for a lot.
"I just tried to weather the storm by mixing it up and running down a lot of balls. But when I got the chance to move her around I made the most of it."
Growing up Dabrowski was a contemporary of current World No.7 Eugenie Bouchard, whose recent success has proved a source of inspiration.
"Having grown up practicing with Genie and seeing what she's done has really motivated me to push through any hard moments in a match and go that extra step," Dabrowski added. "In the past, if it got tough, or it wasn't working, I started to lose focus and today I didn't do that, which I'm really pleased about."
While Giorgi was seeing her title hopes slowly slip away, the only other seed left standing in the bottom half, María-Teresa Torró-Flor, was making a far brisker exit. The No.7 seed lasted just 57 minutes against Julia Goerges, going down 6-2, 6-0.
Remarkably, these two defeats meant that from the original eight seeds just Annika Beck had made it through to the second round. However, before the day was out she also bit the dust, coming within two points of a quarterfinal place only to lose 2-6, 6-4, 7-6(2) to Lara Arruabarrena.