On a filthy night in Dortmund at a packed Signal Iduna Park in front of a sell-out 80,720 crowd, the home side picked up three more points to open the seven-point lead over second-place Mainz ahead of this weekend's matches.
Dortmund are flying high at the moment this was their tenth league win of the season. Their defeat to Leverkusen back in August on the first day of the season is the only blot on their copybook this term.
"It was very difficult for us against an oppoent who played so defensively," said Dortmund coach Jurgen Klopp.
"It took us a while to get into the game, but things worked better for us after the break.
"Hamburg came back into the game late on, which made life hard for us.
"But we are very happy with the win."
The hosts had plenty to celebrate in midweek when uncapped defender Marcel Schmelzer, 22, and 18-year-old midfielder Mario Goetze were called into the German squad along with striker Kevin Grosskreutz and defender Mats Hummels.
Goetze wasted the best chance of the first half when Schmelzer fired in a cross, but the teenager could not connect cleanly with the chance and the opportunity went begging.
With his side top of the league, coach Jurgen Klopp seems to be feeling the pressure when he clashed angrily with the fourth official when a decision went against his side in the first-half.
Barrios compounded Hamburg's misery when he tapped home a cross from Grosskreutz on 70 minutes after Dortmund had ripped apart the Hamburg defence.
The defeat leaves Hamburg seventh in the table.
Source: AFP Global Edition