Having lost eight matches in a row the Australian also trailed Italian wild card Martina Trevisan 2-0 in the final set but rallied to win 6-4 0-6 6-3 in six minutes over two hours.
Gibson, who was ranked 112 two months ago but has shot up 50 places after strong showings at Indian Wells and Miami, is still to find her feet this clay swing.
But on Monday on her Rome debut she dug in when it mattered against Trevisan, whose lowly ranking (516) belies her ability. She was world No.18 three years ago before encountering injury problems.
In front of a thin crowd on a cold day in the Italian capital Gibson lost the second set in 33 minutes and suffered an early break but won the last four games to secure victory.
Gibson now faces Russian 19th seed Diana Shnaider who won their only previous meeting, at this year's Australian Open, in three sets.
Two Australian women are in action on Tuesday.
Ajla Tomljanovic, currently ranked 88 in the world, also meets a local wildcard, 20-year-old Noemi Basiletti, ranked 357.
Daria Kasatkina has a tougher task against American Caty McNally, ranked 14 places higher at 52. The victor meets three-time Rome winner Iga Swiatek, the fourth seed.
Australian No.1 Maya Joint, who is seeded 29, has been given a bye into the second round.
Elsewhere on the opening day of main draw play Barbora Krejcikova defeated Elsa Jacquemot 6-2 6-4 to book a tie with world No.1 seed Aryna Sabalenka.
Anastasia Zakharova survived five match points to beat Dayana Yastremska 4-6 7-5 7-6 (8-6) while Bianca Andreescu and Qinwen Zheng were among others to progress.
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