The pair climbed over locked gates to take control of the theme park's Blue Flyer ride shortly after 04:00 BST.
They flicked the switch and took a trip on the 82-year-old ride before they also raided a cafe, the Blackpool Gazette reported.
A 15-year-old boy was given a community resolution order following Friday's break-in.
A statement from Blackpool Pleasure Beach said: "They managed to operate the ride some time before security patrols discovered them at 04:50.
"From CCTV footage we understand the intruders were at the ride for up to 30 minutes.
"During this time two youths can be seen on the ride."
The statement added: "Following the break-in, the ride has been fully inspected and is operational and open to the public."
The Blue Flyer, based in the Nikelodeon Land section of the theme park, is a wooden rollercoaster designed for children.
Built in 1934, the ride lasts for 90 seconds and travels at a top speed of 15mph.
Community resolution orders are a way of dealing with low level crimes which do not result in the offender going to court or receiving a criminal record, Lancashire Police said.
Two teenagers took an early-hours rollercoaster joyride after breaking in to Blackpool Pleasure Beach.