The Holland midfielder despatched a fine effort into the top-left corner from outside the box in the 24th minute.
The result lifted HSV to sixth spot in the standings - four points ahead of ninth-placed Gladbach - after 22 games.
Neither team showed much going forward in the opening stages, with a long-range blast from Hamburg midfielder Dennis Aogo - which flew inches wide in the 18th minute - the best early chance.
The hosts took the lead after 24 minutes, though, with a stunning strike from Van der Vaart. The former Real Madrid and Tottenham playmaker unleashed a fierce drive from almost 30 yards which arrowed into the top corner of Marc-Andre ter Stegen's net.
Gladbach midfielder Juan Arango prevented the hosts from doubling their lead in the 52nd minute when he blocked a shot by Slobodan Rajkovic, who had been supplied by a Van der Vaart free-kick.
The visitors finally had an opportunity after 69 minutes but Mike Hanke lashed wide from six yards following Patrick Herrmann's cross from the right.
Gladbach again went close with four minutes left, Filip Daems firing just wide from 16 yards.
Hamburg could have put the result beyond doubt in the 90th minute but Marcus Berg sent his attempt over the bar from eight yards following Artjoms Rudnevs' headed pass.