Time trial specialist Tarling completed the course in 16 minutes seven seconds then faced an agonising wait for 58 riders, including other stage favourites and overall contenders, to finish.
“I can’t believe it, I’m so happy,” said Tarling.
“The wait was not nice, I don’t want to do it again, it was a long day for 13km.”
Tarling is now the youngest winner of a time trial in Giro history and has a chance for another time trial victory on stage 10 on 20 May.
Britain’s Ethan Hayter finished ninth on the stage, 14 seconds back on Tarling.
Though he missed out on the stage win, 2023 Giro champion Roglic, 35, gained time over his rivals for the title.
Spain’s Juan Ayuso is now 16 seconds down on Roglic, with Italy’s Antonio Tiberi nine seconds further back.
British twins Simon and Adam Yates, Ecuador’s Richard Carapaz and Colombia’s Egan Bernal are all over 30 seconds down on Roglic but there is plenty of climbing to come in the three-week stage race.
Pedersen went out last and almost held on to the leader’s jersey, missing out by two seconds as he finished seventh, 11 seconds back on Roglic.
A hilly 160km route on Sunday’s stage three, starting and finishing in Vlore, marks the end of the race in Albania before it moves to Italy following Monday’s rest day.
