The 31-year-old, twice a semi-finalist at the All England Club, failed to capitalise on her early momentum after taking a 4-0 lead, and Snigur made her pay by battling back to take the opening set with little fuss.
World number 77 Snigur's flat hitting helped her break in the fifth game of the second set as the pressure began to mount on Svitolina, whose challenge appeared to fade even faster as the sun began to set over the western stands.
Snigur reeled off the games to claim her first top-10 win since 2023 in only 68 minutes and set up a meeting with French qualifier Leolia Jeanjean in the next round.