
Szabolcs Huszti opened the scoring from the penalty spot late in the first half for mid-table Hanover before Olic salvaged a draw in the 70th minute for Hamburg, who have not beaten Hanover at home in now five matches.
Hamburg dropped from third to fourth place as Bayer Leverkusen got a 3-2 comeback victory at lowly Energie Cottbus to move ahead on goal difference.
Elsewhere, Czech starlet Martin Fenin had a sensational Bundesliga debut as the new hiring scored a hat-trick in Eintracht Frankfurt's 3-0 triumph at Hertha Berlin.
Munich won 2-1 at Hansa Rostock on Friday night in the first match after the winter break to lead the way with 39 points. Werder Bremen have 36 ahead of a Sunday home game with VfL Bochum, Hamburg have 33, with Leverkusen and SC Karlsruhe on 31 apiece.
Coming off an easy 3-0 cup win at lower-league Essen, in-form Hamburg were tipped to beat Hanover, but the visitors were sharper early on.
Huszti gave them a deserved lead on a 40th minute penalty, drilling the ball into the right corner after Guy Demel was ruled to brought down Christian Schulz.
Huszti hit the outside left post in the 54th before the hosts finally made it 1-1 from Olic, the Croatian striker tapping into the empty net after a first shot from captain Rafael van der Vaart was saved by goalkeeper Robert Enke.
Hanover had Sergio Pinto sent off in the final minute for kicking out at Nigel de Jong.
"We weren't convincing. We got off to a bad start but improved after the break. It's a pity we didn't get three points and had to be content with one points," said de Jong.
There was more entertainment in Cottbus, where the hosts led after 14 minutes from a header by former Leverkusen player Michel Papadopoulos.
Simon Rolfes grabbed the equalizer in the 59th and substitute Dmitri Bulykin made it 2-1 for Leverkusen in the 68th.
Cottbus bounced back from Christian Bassila in the 77th and had two goals disallowed for offside. But Leverkusen had the last laugh as Rolfes fired home an 86th-minute penalty for the winner.
MSV Duisburg remained last because they blew a 3-1 lead in a 3-3 deadlock with Borussia Dortmund, Diego Klimowicz salvaging the draw with his second goal of the day two minutes into stoppage time.
SC Karlsruhe defeated 10-man Nuremberg 2-0 and VfL Wolfsburg prevailed 1-0 at Arminia Bielefeld.
Fenin, meanwhile, signed from Teplice in January for an estimated 3.5 million euros (5.2 million dollars), was an instant hit for Frankfurt, on target in the 39th, 60th and 90th for a sensational Bundesliga debut against harmless Hertha.
"He won't be measured by goals but he can be really satisfied with his match today. But we are aware that he will have poorer showings as well," said Frankfurt coach Wolfgang Funkel of the 20-year-old talent Fenin.
DPA