Kevin Grosskreutz and Mario Gotze, two of the revelations as Dortmund's previously underrated squad won last season's title, scored in the first half as the hosts started where they left off in May.
Grosskreutz, 23, added the third early in the second half as a packed crowd of nearly 80,000 were treated to some superb attacking football from the hosts.
Dortmund, whose starting line-up had an average age of just over 23, eased off after that and Hamburg, eighth last season, pulled one back through Robert Tesche.
"We played opponents today who were simply a class above us," said Hamburg captain Heiko Westermann.
Hamburg coach Michael Oenning agreed.
"Borussia Dortmund today play in a different league, their passing of the ball was extremely good," he said.
Japan midfielder Shinji Kagawa had the first effort of the match for Dortmund with a rasping drive which flew over in the 13th minute.
The hosts went ahead midway through the first half when Gotze found Grosskreutz on the left and he finished a typically flowing move by rolling a low shot into the net off the far post.
Dortmund shrugged off the absences of Nuri Sahin, last season's playmaker who has been sold to Real Madrid, and injured Paraguay striker Lucas Barrios, their top scorer last season, as they tore the Hamburg defence apart.
Kagawa hit the post and then fired wide after Grosskreutz pulled the ball back as Jurgen Klopp's team played some delightful one-touch football capped by a brilliant second goal in the 28th minute.
RETURN PASS
Gotze broke down the middle and played the ball to Robert Lewandowski, who backheeled a return pass to split the defence and left the 19-year-old to slot the ball home.
Hamburg's woes deepened when Peru striker Paolo Guerrero, top scorer in last month's Copa America with five goals, limped off injured before the break.
Dortmund needed only three minutes of the second half to increase their tally after another quick exchange of passes involving Gotze and Kagawa ended with Grosskreutz scoring at the second attempt after his first effort had been blocked.
Tesche fired in after a goalmouth scramble and Hamburg, with a late flourish, nearly scored again in the next attack when Marcel Jansen's shot was just saved by Roman Weidenfeller.
