French rising star Garcia fell at the first hurdle in Moscow as Serbian wildcard Krunic won 6-4 6-2 in just 53 minutes.
Moscow-born Krunic, ranked 109 in the world, will face Tsvetana Pironkova in the second round after taking all four break points that came her way in a clinical display.
Garcia was on the back foot when Krunic broke in the third game of the match, but the world number 36 responded immediately by breaking to love.
The underdog took that setback in her stride and went on to secure a crucial second break to lead 5-4 and duly served out the set.
Garcia was unable to respond in the second set, as Krunic took the upper hand by breaking to lead 2-1 and then pressed home her advantage with another break to go 4-1 up.
There was no way back for Garcia and Krunic served out the match to ease into the second round.
Sixth seed Anastasia Pavlyuchenkova had no such trouble on home soil as she beat Ana Konjuh 6-3 6-4.
World number 30 Pavlyuchenkova was made to work for her victory, thwarting the Croatian by saving six break points as her three breaks proved to be enough to progress.
Camila Giorgi, ranked 39 in the world, breezed through in the final game of the day as qualifier Lesia Tsurenko was beaten 6-0 6-3 in only 55 minutes.
There was disappointment for Elena Vesnina, as the Russian suffered a shock defeat 6-2 6-2 against Katerina Siniakova - another qualifier.
Vitalia Diatchenko will feature in the second round after Olga Govortsova retired when she was trailing 6-2 2-1, while Kateryna Kozlova beat Aliaksandra Sasnovich 6-3 6-2.
Ajla Tomljanovic also secured her place in the second round on Tuesday by seeing off Alexandra Panova 6-4 4-6 6-3.