Leipzig went into the game looking to close the gap on the top four and got off to a fast start, as Romulo Cardoso stung the palms of Daniel Heuer Fernandes early on.
It was an end-to-end affair, with the home side going close when Damion Downs forced a save out of Maarten Vandevoordt, who got down low to deny the USA international.
The home side were dealt a blow with Nicolas Capaldo forced off through injury just before the midway point of the first half, but they soon put that behind them, breaking the deadlock minutes later.
After forcing a turnover on the halfway line, Hamburg broke forward, and Fabio Vieira finished off a swift team move, firing past Vandevoordt for his second goal in as many games.
Leipzig responded well to going behind and almost immediately equalised through Christoph Baumgartner, but the Austrian’s header flashed narrowly wide.
Brajan Gruda was next to go close for Die Roten Bullen, and the visitors’ pressure told as they levelled the contest in the 36th minute.
A cross to the back post was chested down by Ridle Baku into Romulo, who, despite having his back to goal, netted with a sublime backheel, beating Heuer Fernandes with an exceptional instinctive finish.
Armed with the momentum, Ole Werner’s men got off to the best possible start to the second half, completing the comeback within five minutes of the restart.
After winning possession in Hamburg’s half again, the hosts were punished following a neat build-up which saw Romulo slip Yan Diomande through, and the talented Ivorian did well to shrug off the pressure of three opposition defenders before slamming into the roof of the net.
Romulo was in the thick of the action for Leipzig and had the opportunity to double his tally for the evening from the penalty spot after Nicolai Remberg was penalised for handball in the box. Romulo stepped up, but his low effort from 12 yards was easily saved by Heuer Fernandes, keeping Hamburg in the contest with a little over half an hour remaining.
Hamburg ultimately failed to capitalise on that reprieve. Instead, the away side looked the likeliest to net again, though Ezechiel Banzuzi missed a header from close range.
That did not come back to bite Leipzig, however, as they claimed just their second win in six Bundesliga games, moving to within two points of the top four as a result.
Hamburg, meanwhile, remain in 11th place but just four points above the relegation places and are now winless in the last six meetings with Leipzig.
Flashscore Man of the Match: Romulo Cardoso (RB Leipzig)
