Croatia striker Olic let fly from 25 metres, scoring in off the far post to settle a breathless clash between two teams who have struggled for consistency this season.
Victory took Hamburg back up to fifth place with 26 points from 14 games. Werder Bremen, runners-up to Bayern Munich last season, remain down in ninth place with 20 points.
Hoffenheim lead the standings with 31 points after winning 3-1 at Cologne on Saturday. Second-placed Leverkusen, beaten 2-1 at Arminia Bielefeld, and Bayern, 4-1 winners over visiting Energie Cottbus, have 28 points apiece.
Hamburg, who have slipped out of the title race, were outplayed by Werder but never stopped running and nicked the win thanks to a piece of brilliance from Olic in the 74th minute.
"We showed passion and fight," Hamburg coach Martin Jol told reporters. "Werder were maybe the better team but they didn't create that many chances."
Hamburg took an early lead when Paolo Guerrero squeezed in a shot at the near post after Tim Wiese had blocked a Mladen Petric free kick.
Diego's sweetly struck free kick brought Werder level midway through the half and, while the visitors were the better side for the remainder of the game, Olic made the difference.
The only negative side to an absorbing match came immediately after Diego's equaliser when Werder captain Frank Baumann was hit by an object apparently thrown from the crowd.
The German FA is likely to investigate.
