The 28-year-old Czech, appearing at the ATP 250 clay-court event in Umag for the first time, earned a hard-fought 6-3 3-6 7-6 (7-2) triumph on Tuesday.
Rosol, ranked 43rd in the world, fired down nine aces and won four of the seven break points that he fashioned as he wrapped up victory in two hours and five minutes.
The first set went with serve until a run of three consecutive breaks which took Rosol into a 5-3 lead and he held his nerve to move ahead.
World number 100 Schwartzman showed character to respond in the second set, winning all five of his service games and claiming the only break to level the match.
Both players were unconvincing on serve again in the decider, but it was Rosol who emerged triumphant from the tie-break as he claimed three mini-breaks to Schwartzman's one to move into the second round.
Sixth seed Andreas Seppi was also taken to three sets as he came out on top in an all-Italian match against Marco Cecchinato.
World number 45 Seppi won 6-2 6-7 (2-7) 6-1, but will be eager to improve his first-serve percentage of 51 if he is to challenge for the title this week.
Carlos Berlocq, seeded eight, got the better of qualifier Andrej Martin 7-6 (7-4) 6-3 as he strives to win his second ATP World Tour title of the season.
Igor Sijsling will face home hope and 2012 champion Marin Cilic in the second round after the Dutchman beat Julian Reister 7-6 (7-2) 6-7 (3-7) 6-2.
There were also victories for Albert Montanes, Horacio Zeballos, Pablo Cuevas, Albert Ramos-Vinolas, Teymuraz Gabashvili and Pere Riba.