At 17 years and 113 days, the midfielder beat the record held by Phil Foden, who plays for Manchester City.
Dortmund were second best in Turin, with Ciro Immobile and a Marwin Hitz own goal giving the home side control.
Erling Braut Haaland gave Dortmund hope but Jean-Daniel Akpa Akpro responded almost immediately to seal Lazio’s win.
The win represents a turn of fortune for Simone Inzaghi’s side, who finished fourth in Serie A last season, but have only won one of their four league matches this season and were beaten 3-0 by Sampdoria on Saturday.
In contrast, Dortmund have had a decent start to this campaign, winning three of their four games in the Bundesliga.
However, they have now lost 10 of their last 14 Champions League away games and have just four wins from 17 matches in Italy.
Bellingham makes history but Lazio have final word
Midfielder Bellingham joined Dortmund from Birmingham this summer.
He had already made himself his new club’s youngest ever goalscorer with his debut goal against Duisburg in the German Cup.
He was unable to make such a lasting impact on Tuesday’s game, although he wasn’t alone in the Dortmund side, particularly in a flat first half that saw the home side seize control of the game.
Immobile had a disappointing single campaign with the German side in 2014-15, during which he managed 10 goals in 34 matches, but since joining Lazio in 2016 he has not stopped scoring.
Last season, he equalled Gonzalo Higuain’s scoring record in Serie A, netting 36 times, and he hit his second goal of this campaign in all competitions courtesy of a close-range finish.
Lazio’s lead was doubled in the 23rd minute when Luiz Felipe, on his return from injury, attacked a corner and got a glancing touch with his head, steering the ball towards the goal though it hit the face of Hitz as it flew in.
Haaland continued his remarkable run of Champions League form with his 11th goal in nine appearances in the competition, but Akpa-Akpro ensured there would be no late home nerves, finishing off a quick counter-attack.
The youngest Champions League player of any nationality is Nigerian Celestine Babayaro, who was 16 years and 86 days when he appeared for Anderlecht against Steaua Bucharest in 1994.
It was a game to forget for the full-back, though, as he was sent off after 37 minutes.
Last season, Barcelona’s Ansu Fati became the youngest Champions League scorer when he hit the winner at Inter Milan at 17 years and 40 days old.
Lazio end long wait for Champions League win
- Lazio picked up their first victory in the Champions League since beating Werder Bremen at home in November 2007 (2-1) – 12 years and 349 days ago.
- Borussia Dortmund have lost each of their last four away Champions League matches versus Italian teams, conceding two or more goals in each defeat.
- Borussia Dortmund have lost four consecutive away games in the Champions League/European Cup for the first time since February 1958, while the fourth defeat in that run also came against Italian opponents (Milan).
- Haaland has scored nine goals in his seven Champions League group stage appearances and 11 goals in nine games across all stages.
- Immobile has scored his first goal in the Champions League since netting for Borussia Dortmund in December 2014. Indeed, he’s the first player to score for and against Dortmund in the competition.