Croatian front man Olic has scored in five of his past six league outings, including their third goal at the Imtech Arena that put them 3-0 up four minutes after half-time.
Dieter Hecking's men held on for all three points to catapult them into the UEFA Champions League play-off spot, but importantly their place in Europe at least is assured - as they cannot fall lower than the two UEFA Europa League spots.
Olic praised his side's ability to break down the relegation-threatened hosts early, with Ivan Perisic's second-minute goal giving Wolfsburg a lead they would not relinquish.
"Scoring early was important for us and a big blow for HSV (Hamburg)," the former Bayern Munich man said.
"You could tell they were under pressure as they made a few mistakes at the back. Thankfully we took full advantage of them.
"We've been playing very well in the last few weeks, which makes life very easy for a striker like me.
"I've been getting into scoring positions and I've managed to take my chances."
Wolfsburg's Brazilian midfielder Luiz Gustavo regretted his sending off in the 90th minute.
"It's a shame about the red card, but it's happened before, so I'm used to the situation. We played very well, though, and I'm happy we got the three points," Gustavo said.
Hamburg's Turkish forward Hakan Calhanoglu agreed with Olic that the early goal was a crucial one.
"The goal in the second minute was decisive. We were expecting a lot more from this game,"
"We wanted to start well, but we didn't manage to do so.
"We knew how strong Wolfsburg are and how well they've been playing of late, but now we have to learn from our mistakes and win our next three games."
Hamburg occupy the relegation play-off spot in 16th, one point shy of Stuttgart - who are safe as it stands - but one point ahead of Nuremberg, who are in the drop zone.
