Leipzig were on the front foot in the opening stages, and they saw plenty of the ball as Die Roten Bullen managed to take the lead with 17 minutes on the clock.
Ezechiel Banzuzi was freed down the right and picked out Tidiam Gomis with his low cross from near the byline, and the forward’s first-time effort found the narrowest of gaps to beat Daniel Heuer Fernandes at his near post.
Hamburg have now failed to keep a clean sheet in any of their last 17 Bundesliga matches, and they were proving ideal opposition for the home side to restore their confidence after a disappointing 4-1 defeat to UEFA Champions League newcomers Como in midweek.
With the half-hour mark approaching, Leipzig doubled their advantage. Antonio Nusa dispossessed Shafiq Nandja 40 yards from goal and advanced to the edge of the area, where the defender’s recovering challenge deflected off Nusa and beyond Heuer Fernandes to compound Hamburg’s woes.
With Die Rothosen failing to register a single shot on target in a disappointing first-half display, the away side needed a significant improvement in the second period.
And they could have halved the deficit four minutes in when David Moller Wolfe collected a loose ball inside the area and saw his near-post effort saved by Maarten Vandevoordt.
Leipzig could have extended their lead on the hour mark as Gomis’ chipped cross from the right side of the area was acrobatically met by Christopher Nkunku, whose effort sailed wide of the right post.
The hosts were in cruise control in the closing stages, and they managed to find a further three goals in a clinical five-minute spell to ensure their victory was a resounding one.
First, Willi Orban headed home Nusa’s free-kick at the far post, shortly before Nkunku fired into the right corner from inside the box to make it four.
Romulo Cardoso then dispossessed Warmed Omari, advanced on goal, and rounded Heuer Fernandes before rolling the ball into an empty net.
This impressive result sees Leipzig climb eight places to fourth for the time being, while Hamburg’s woes continue as they drop to the foot of the table, having suffered a third consecutive defeat, with Merlin Polzin’s men still awaiting their first goal and point of the campaign.
Flashscore Man of the Match: Antonio Nusa (RB Leipzig)