Ibricic's lofted shot from 25 metres after Dinamo goalkeeper Tomislav Butina miscued a clearance into his path settled the semi-final second leg between Croatia's two biggest clubs after a goalless first leg in Zagreb.
Hajduk will play NK Sibenik in the showpiece. Sibenik reached their first final after beating Varteks Varazdin 2-0 away despite playing most of the return leg with 10 men, following a 0-0 draw in the reverse fixture.
Sibenik defender Velimir Vidic was sent off in the first half for two bookable offences, a foul followed by dissent, but the visitors always looked more likely to score and took a 75th-minute lead thanks to a solo effort by Ermin Zec.
Ivan Fustar sealed victory with a 90th-minute scorcher from 25 metres, exacting sweet revenge for their 5-1 league defeat to Varteks last weekend.
"We have come a long way to reach the Cup final, from non-league football to surviving in the top flight by the skin of our teeth and it is an incredible feeling," Sibenik president Goran Pauk told Croatian media.
"This is fitting reward for our hard work, we wanted it more than Varteks and we are looking forward to a chance of winning the first trophy in the club's history," he said.
