The 18-year-old Luton diver led the way after the first dive before slipping to sixth after the halfway point, but a well-executed final dive helped her sneak into the podium positions.
Rollinson's two-and-a-half piked forward somersault scored a trio of 7.5s to win her the bronze medal with a total of 272.00 points, fending off competition from Scotland's defending champion Grace Reid, who placed fourth with 268.15.
"I was just expecting to turn up and have a bit of experience in an individual event, because I have only ever done two proper internationals, let alone an individual senior event. So to get this is crazy," Rollinson told BBC Sport.
"I genuinely think the crowd helped. Just standing on the board it's so nice to hear so many people cheering for you, trying to get you to do well.
"It's been hard the past few weeks trying to train and deal with everything so it's just nice to come away with something."
The gold medal went to Mia Vallee of Canada with 291.85 points, and Australia's Brittany O'Brien scored 279.60 to take the silver. Rollinson's compatriot Yasmin Harper managed to recover from an underwhelming second dive to finish seventh with 254.50. body check tags ::