The towering Chinese matched a feat previously achieved only by Grant Hackett when he romped to the 400 metres freestyle title on Sunday, becoming only the second man after the Australian to claim world titles at 400, 800 and 1,500 metres.
While Sun's three titles have come at two different championships - he won the 800 and 1,500 in Shanghai two years ago and was second in the 400 - he is on course to match Hackett's three golds from the 2005 edition in Montreal.
"I feel good, the kind of feeling you always have in the preliminaries," Sun, gold medallist at 400 and 1,500 metres at last year's London Olympics, told reporters.
The 22-year-old said he was not thinking about breaking Zhang Lin's world record for the 800, which is not an Olympic event, which his compatriot set in Rome in 2009 with the aid of a now-banned non-textile suit.
Sun was second-quickest in the 800 heats on Tuesday behind Connor Jaeger of the United States, with Canada's Ryan Cochrane, silver medallist in Shanghai and third at the Rome world championships in 2009, third fastest.
In the morning's other heats, Frenchwoman Camille Muffat set the pace in the women's 200 metres freestyle ahead of Hungary's Katinka Hosszu, gold medallist in Monday's 200 metres individual medley, and world-record holder Federica Pellegrini.
Pellegrini is swimming the event in Barcelona despite saying before the championships that she was focusing on the 200 metres backstroke.
American teenager Missy Franklin, who is swimming eight events including relays, was fifth fastest.
South Africa's Chad le Clos caused a sensation when he beat decorated American Michael Phelps to win 200 metres butterfly gold in London and he was second-quickest in the heats for the event here, behind American Tyler Clary.
In the men's 50 metres breaststroke, another non-Olympic distance, Cameron Van Der Burgh of South Africa swam 0.11 seconds outside his own world record to top the heats.
Australian Christian Sprenger, who beat Van Der Burgh into second to win the 100 metres breaststroke gold on Monday, was fourth quickest in 27.30.
Italy's Fabio Scozzoli, silver medallist at the last world championships in Shanghai, did not qualify.