Andre Schuerrle and Florian Heller scored the late goals that secured a come-from-behind victory for Mainz, who are chasing a top three finish for a Champions League place.
Hamburg were extremely lucky to take the lead through Marcell Jansen's shot from 12 metres came down off the bar but clearly did not cross the line as TV replays showed.
The home side's luck ran out in the second half though when Schuerrle and Gojko Kacar's own goal either side of Mladen Petric's 59th minute strike saw Mainz level.
The 20-year-old Germany international then threaded a precise pass between Rost and two defenders for Heller to tap in Mainz's fourth goal two minutes from time.
In Sunday's early game, late goals from Peruvian Claudio Pizarro and Marko Marin gave Werder Bremen a 3-1 victory at mid-table Freiburg to move out of the relegation zone.
"We finally managed to get three points. You need recognition for your work and we have not had that recently," said Bremen coach Thomas Schaaf.
But with eighth-placed Freiburg increasing the pressure late in the game, Marin broke free, fed Pizarro with a well-timed pass and the Peruvian, who is the Bundesliga's all-time top foreign scorer, fired in a low drive after 76 minutes.
Germany international Marin turned scorer deep in stoppage time to seal Bremen's first win since mid-January.
